Dia: Dimecres, 7 de setembre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Vered Rom-Kedar. The Weizmann Institute, Rehovot, Israel

Títol: Billiard like potentials - theory and applications

Resum: What kind of of solutions do multi-dimensional nonlinear Hamiltonian systems admit? This is a difficult open question, especially when far from integrable systems are considered. We develop a paradigm for studying this question for a class of Hamiltonian systems : smooth mechanical systems with potentials that may be decomposed to a sum of an integrable part and of a steep potential part [1,2].

Three applications of this paradigm will be discussed:- The destruction of ergodicity in some multi-dimensional smooth steep systems that limit to uniformly hyperbolic multi-dimensional dispersing billiards and its relation to the Boltzmann ergodic hypothesis [3].
- Simple models for tri-atomic co-linear reactions and other scattering systems [4,5].
- Robust particles accelerators [6].

- A. Rapoport, V. Rom-Kedar and D. Turaev, *Approximating multi-dimensional Hamiltonian flows by billiards, Comm. Math. Phys., 272(3), 567-600, 2007.*
- M. Kloc and V. Rom-Kedar, in preparation.
- A. Rapoport, V. Rom-Kedar and D. Turaev, *Stability in high dimensional steep repelling potentials Comm. Math. Phys., 279, 497-534, 2008.
- L. Lerman and V. Rom-Kedar, A saddle in a corner - model of collinear chemical reactions, submitted, 2011.
- A. Rapoport and V. Rom-Kedar, *Chaotic scattering by steep potentials*, Phys. Rev E., *77*, 016207 (2008).
- V. Gelfreich, V. Rom-Kedar, K. Shah, D. Turaev, Robust exponential accelerators PRL 106, 074101, 2011 Abstract at PRL

Dia: Dimecres, 14 de setembre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Albert Granados, Universität Stuttgart

Títol: Melnikov method for subharmonic orbits and heteroclinic connections in a non-smooth system

Resum: In this work we consider a two-dimensional piecewise smooth system, defined in two sets separated by the switching curve

x=0 . We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits connecting two critical saddle points located at each side ofx=0 . Finally, we assume that the region closed by these heteroclinic connections is fully covered by periodic orbits surrounding the origin, whose periods monotonically increase as they approach the heteroclinic connection.When considering a non-autonomous (T-periodic) Hamiltonian perturbation of amplitude

ε , using an impact PoincarÃ© map, we rigorously prove that, for every n and m relatively prime andε>0 small enough, there exists an T-periodic orbit impacting2m times with the switching curve at every period if a modified subharmonic Melnikov function possesses a simple zero. In addition, we also prove that, if the orbits are forced to undergo a discontinuity when they crossx=0 , which simulates a loss of energy, then all these orbits persist if the relative size ofε>0 with respect to the magnitude of this jump is large enough.We also obtain similar conditions for the splitting of the separatrices.

Dia: Dimecres, 21 de setembre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Heinz Hanβmann, Mathematisch Instituut, Universiteit Utrecht (Holanda)

Títol: On the destruction of resonant Lagrangean tori in Hamiltonian Systems

Resum: Poincaré's fundamental problem of dynamics concerns the behaviour of an integrable Hamiltonian system under a (small) non-integrable perturbation. Under rather weak conditions K(olmogorov)A(rnol'd)M(oser) theory settles this question for the majority of initial values. The perturbed motion is (again) quasi-periodic, the number of frequencies equals the number of degrees of freedom. KAM theory proves such Lagrangean tori to persist provided that the frequencies are bounded away from resonances by means of Diophantine inequalities.

How do Lagrangean tori with resonant frequencies behave under perturbation? We concentrate on a single resonance, whence many

n -parameter families ofn -tori are expected to be generated by the perturbation; heren+1 is the number of degrees of freedom. For non-degenerate systems we explain the pattern how these families of lower-dimensional tori come into existence, and then discuss what happens in the presence of degeneracies.

Dia: Dimecres, 28 de setembre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Krzysztof Baranski, University of Warsaw

Títol: On the Hausdorff dimension of the Sierpinski Julia set

Resum: We consider rational maps on the Riemann sphere of the form

*F*,_{λ}(z) = z^{n}+ λ/z^{n}*λ∈*,**C***n∈*, which can be regarded as singular perturbations of the polynomial**N***z*. It is known that for some parameters the Julia sets of such maps are homeomorphic to the Sierpinski carpet. We estimate the Hausdorff dimension of the Julia sets of these maps for some parameters.^{n}

Dia: Dimecres, 5 d'octubre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Pau Rabassa, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen

Títol: Towards a renormalization theory for quasi-periodically forced one dimensional maps

Resum: This talk focusses on the study of quasi-periodically forced one dimensional unimodal maps. These are maps on the cylinder where the periodic component is a rigid rotation and the other component is a quasi-periodic perturbation of a map in the interval. For certain one parametric families of maps in the interval, it is well known that their bifurcations exhibit a universal behavior, in the sense that the behavior is the same for a wide class of families. This universal behavior can be explained as a consequence of the dynamics of the renormalization operator. We discuss what happens to this phenomenon when we add a q.p. perturbation to the one dimensional family of maps. Concretely we show numerical evidences of self-similarity and universality. We also propose an extension of the renormalization operator to the q.p. forced case, which gives a suitable explanation to the previous numerical observations

Dia: Dimecres, 19 d'octubre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Sergey V. Gonchenko, Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia

Títol: Towards scenarios of chaos appearance in three-dimensional maps

Resum: We analyze chaotic dynamics of three-dimensional smooth dissipative maps (diffeomorphisms). We show that two main bifurcation scenarios of chaos developing (from an asymptotically stable fixed (periodic) point to a strange attractor) can be typically occurred here. In the first scenario, the spiral (Shilnikov) attractor appears, whereas, in the second one, either Lorenz-like or a "figure-8" strange attractors can be observed. We give a qualitative description of both these scenarios and illustrate them by some numerics (for 3D Henon maps).

Dia: Dimecres, 26 d'octubre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Dimitry Turaev

Títol: Arnold diffusion in a priori chaotic systems

Resum: We show that given a Hamiltonian system with a chaotic behaviour (a transverse hooclinic orbit) in every energy level an arbitrarily small non-autonomous generic real-analytic perturbation creates orbits of unbounded drift in the energy.

Dia: Dimecres, 9 de novembre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Juan J. Morales, Universidad Politécnica de Madrid

Títol: On the Integrability of Polynomial Fields in the Plane by means of Picard-Vessiot Theory

Resum: We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. We also study the Poincaré problem for some of the families.

(joint work with P. B. Acosta-Humánez, J.-Tomás Lázaro and C. Pantazi)

Dia: Dimecres, 16 de novembre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Oriol Castejón, Universitat Politècnica de Catalunya

Títol: Breakdown of Heteroclinic Orbits for Analytic Unfoldings of the Hopf-Zero Singularity. The Singular Case

Resum: We study the exponentially small splitting of a heteroclinic connection in a two-parameter family of analytic vector fields in R

^{3}, which arises from analytic unfoldings of the Hopf-zero singularity. Previous work showed that, in a conservative setting, this heteroclinic connection is destroyed if one considers perturbations of a higher order (the so-called regular case), and an asymptotic formula of the distance between the stable and unstable manifolds when they meet at the plane*z=0*was given. Moreover, its main term was a suitable version of the Melnikov integral. Here, we study the singular case in both the conservative and dissipative settings, and we show that Melnikov theory is no longer valid. We give an asymptotic expression of the splitting distance, which is exponentially small with respect to one of the perturbation parameters.The reason to study the breakdown of the heteroclinic orbit is that it can lead to the birth of some homoclinic connection to one of the critical points in the unfoldings of the Hopf-zero singularity, producing what is known as a Shilnikov bifurcation.

This is a joint work with I. Baldomà and T. M-Seara.

Dia: Dimecres, 23 de novembre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Mercè Ollé, Universitat Politècnica de Catalunya

Títol: Dynamical systems tools to study a hydrogen atom

Resum: We consider the problem of the hydrogen atom interacting with a circularly polarized microwave field, modelled by a perturbed Kepler problem. In this talk, we concentrate mainly in three parts: the first one concerning the general features of the CP problem, the second one is related to the description of the dynamics from a global point of view (taking into account the main invariant objects), and finally we study the ionizing orbits, that is orbits that escape to infinity.

This is a joint work with E. Barrabés, F. Borondo, D. Farrelly and JM. Mondelo

Dia: Dimecres, 30 de novembre de 2011.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Inna Basak, Universitat Politècnica de Catalunya

Títol: Bifurcation analysis of Rubanovskii system via bi-Hamiltonian approach

Resum: We discuss about some properties of bifurcation diagram of the gyroscopic generalization of the Steclov-Lyapunov integrable case of Kirchoff equation - Rubanovskii system, describing the motion of a gyrostat in an ideal fluid. Using the fact that Rubanovskii system is a bi-Hamiltonian system and applying techniques for analysis of singularities of bi-Hamiltonian system developed by A.Bolsinov, A.Oshemkov we solve the following problems: description of the singularities of the momentum mapping defined by four first integrals of the system, stability analysis for closed trajectories, non-degenaracy and stability analysis for equilibria.

Dia: Dimecres, 7 de desembre de 2011.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Heinz Hanssmann, Mathematisch Instituut, Universiteit Utrecht (Holanda)

Títol: Quasi-periodic bifurcation theory

Resum: Invariant tori with quasi-periodic dynamics often allow to better understand the behaviour of a dynamical system. Their complexity ranges between equilibria and periodic orbits on the one side and more complicated structures of dynamics like strange attractors on the other side.

To capture the dynamics on quasi-periodic tori one should introduce parameters; both tori with dense orbits and completely resonant tori consisting of periodic orbits correspond to dense subsets of the parameter space. Under variation of parameters bifurcations can occur.

In dissipative dynamical systems the parameters are external (e.g. think of the Reynolds number, then repeated Hopf bifurcations might explain the onset of turbulence) while in Hamiltonian systems the parameters are the actions conjugate to the toral angles. Other contexts to which the theory applies include volume-preserving and reversible systems.

Dia: Dimecres, 11 de gener de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Joan Sánchez Umbría, Departament Física Aplicada, UPC.

Títol: An overview of the computation of invariant manifolds for PDE's.

Resum: The continuation of fixed points of large-scale dynamical systems (ODE/DAE) obtained by discretizing systems of elliptic and/or parabolic PDE has been a common tool used by researchers in Nonlinear Elasticity and Fluid Mechanics since the late seventies. The efficient computation of other invariant objects by other means than just time evolution is very recent. Algorithms based on Newton-Krylov techniques used to compute periodic orbits, invariant tori, and 2D unstable manifolds of periodic orbits will be presented. I will focus on the implementation of the multiple shooting algorithm for periodic orbits, and on the comparison of two algorithms for the computation of invariant tori.

Dia: Dimecres, 18 de gener de 2012.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Alejandro Luque, Universitat de Barcelona.

Títol: Dinámica de cargas eléctricas en campos mágneticos ABC

Resum: Los campos ABC son una familia de campos de Beltrami sobre en el toro T^3 que tiene interés en problemas de magneto-hidrodinámica. En esta charla discutiremos algunas propiedades elementales de la dinámica de cargas eléctricas sometidas a este campo particular. En general, el problema viene dado por un hamiltoniano de 3 DOF que se reduce a 2 DOF para algunos valores de los parámetros.

Por un lado, estudiaremos la dinámica local para el problema de 2 DOF entorno de cuatro puntos de equilibrio y de una curva degenerada de puntos críticos. Para demostrar la existencia de soluciones casi-periódicas cerca de ésta última, usaremos unas coordenadas adaptadas a la curva y deformaremos la forma simpléctica de forma adecuada.

Por otro lado, estudiaremos aspectos de no integrabilidad en este problema usando teoría de Morales-Ramís y estudiando la escisión de separatrices de toros normalmente hiperbólicos.

Si el tiempo lo permite, discutiremos la existencia de una variedad normalmente hiperbólica donde usar la teoría geométrica de difusión de Arnold en sistemas a priori inestables.

Este es un trabajo conjunto con Daniel Peralta-Salas.

Dia: Dimecres, 1 de febrer de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Pablo S. Casas, UPC

Títol: Clasification of symmetric periodic trajectories of billiards inside ellipsoids

Resum: We find and classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside nondegenerate ellipsoids of

*R*for^{n+1}*n=1,2*. SPTs are periodic trajectories passing through some symmetry set. We prove that there are exactly*2*classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (^{2n}(2^{n+1}-1)*n=1*) and each of the 112 classes in the 3D case (*n=2*). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display the 12 classes in the 2D case and a selection of 3D minimal SPTs.This is a joint work with Rafael Ramírez Ros.

Dia: Dimecres, 8 de febrer de 2012.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Ivan I. Ovsyannikov, Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia

Títol: Global bifurcations of 3D diffeomorphisms with non-rough homoclinic and heteroclinic trajectories

Resum: Global bifurcations leading to appearance of stable periodic orbits, invariant tori and strange attractors in multi-dimensional dynamical systems are studied. These problems attract high interest provided by recent discovery of strange attractors of a new type: wild hyperbolic attractors. This kind of strange attractor, unlike well-known Lorenz attractor and hyperbolic attractor allows homoclinic tangencies inside it but, of course, as a true strange attractor does not contain stable periodic orbits. Another important property of such attractors is that they can be met in applications and models. The examples are: spiral attractor in the Turaev-Shil'nikov model, attractors obtained as periodic perturbations of Lorenz-like systems etc. But when observing an attractor in application, it is hard (or even impossible when using numerical methods only) to distinguish true strange attractor from a quasiattractor (which can contain stable orbits).

Some cases related to this problem are considered. Namely, bifurcations of homoclinic tangencies to saddle and saddle-focus fixed points of a neutral type are investigated. It is shown that these cases are principally different. Explanation of the "invisibility effect" of stable periodic orbits in one-parametric families is provided. Regarding the heteroclinic bifurcations, a contracting-expanding case of a contour consisting of two saddle-foci is investigated. It is shown that there may co-exist an infinite number of wild hyperbolic Lorenz-like attractors.

Dia: Dimecres, 15 de febrer de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m
A càrrec de: Mike Jeffrey

Títol: Dynamics of nonsmooth systems: bifurcations, singularities, and explosions

Resum: The behaviour of nonsmooth systems have seen growing interest in recent years, motivated by models from industrial mechanics and electronics, from ecology, and from neuroscience. Local dynamics at a discontinuity can now be classified geometrically, using a small family of fundamental singularities and bifurcations. Moreover, these allow us to classify global dynamics in the form of sliding bifurcations. It also reveals more novel phenomena, such as discontinuity-induced explosions, which occur when determinism breaks down inside a well-defined nonsmooth flow. The geometry behind all of these suggests a fundamental link between nonsmooth systems, and the dynamics of (smooth) singularly perturbed systems, which we access through an approximation method called 'pinching'.

Dia: Dimecres, 22 de febrer de 2012.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Carles Simó, Universitat de Barcelona

Títol: A global study of 2D dissipative diffeomorphisms with a homoclinic figure-eight

Resum: We consider 2D diffeomorphisms having a dissipative saddle and a figure-eight formed by its manifolds. They are simplified models of phenomena with forcing and dissipation. Under generic perturbations the manifolds can split undulate. This gives rise to different transversal homoclinic points and to a large set of bifurcations.

It should be emphasized that a main goal is to figure out the global behavior. Not only what happens close to a given bifurcation, but to study which kind of dynamical phenomena appear in a fundamental domain which captures all the non-trivial facts. We will present the main tools to study the bifurcation diagram (topological methods, quadratic and cubic tangencies, return maps, cascades of sinks,...) giving rise to different kinds of attractors. The analysis is illustrated by the numerical study a model which, despite being simple, has a ``universal'' character. All the phenomena predicted by the theoretical analysis are seen to be realized in the model. Directions for future work will be outlined. This is a joint work with S. Gonchenko and A. Vieiro.Dia: Dimecres, 29 de febrer de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 15h45 Café i galetes
- Hora: 16h

A càrrec de: Sergey Gonchenko

Títol: On regular and chaotic dynamics of "celtic stone"

Resum: We study stable dynamics (both regular and chaotic) of the well-known mechanical system "celtic stone" (called sometimes as "celt" or "rattleback", or "wobblestone", or even "Russian stone"). Physically, it is a canoe-shaped rigid body with the curious property of spin asymmetry: it tends to have the stable vertical rotation in one direction only, independently on initial conditions for rotation. In the talk we try to explain this dynamical property by means of some mathematical idealization - the nonholonomic model of celtic stone. We study this model by numerical and qualitative methods and describe various stable regimes: permanent rotation, oscillations and, finally, chaotic dynamics.

Dia: Dimecres, 7 de març de 2012.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Elisa Maria Alessi, Universita di Pisa

Títol: Orbit determination and parameter estimation for the radioscience experiments of the BepiColombo mission

Resum: The BepiColombo mission to Mercury is an ESA/JAXA joint project with very challenging objectives regarding geodesy, geophysics and fundamental physics. The Celestial Mechanics Group of the University of Pisa is responsible for the orbit determination of the Mercury Planetary Orbiter (MPO) and the parameter estimation corresponding to the radio science experiments. With this, we mean the gravimetry, rotation and relativity experiments based on very accurate range and range-rate observations. In this talk, we will describe the experiment and explain how the orbit determination is performed. In particular, we apply a non linear least squares differential correction fit on a set of observational arcs separated by intervals of time where the MPO is not visible. The constrained multi-arc strategy is able to link subsequent arcs in a smooth way, to solve for variables belonging or not to the tracking intervals and mitigate problems due to degeneracies or modeling limitations.

Dia: Dimecres, 21 de març de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 15h45 Café i galetes
- Hora: 16h

A càrrec de: Erwin Suazo, University of Puerto Rico at Mayaguez

Títol: On Solutions for Linear and Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians

Resum:
For nonlinear Schroedinger equation with variable coefficients we
construct soliton-like solutions for certain choices of the coefficients,
including important examples such as bright and dark solitons and Jacobi
elliptic and second Painlevé transcendental solutions, which are
important for current research in nonlinear optics and Bose--Einstein
condensation. Also we show an example of existence of ^{∞}

Dia: Dimecres, 28 de març de 2012.

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Zubin Olikara, University of Colorado

Títol: Computing quasi-periodic tori and associated manifolds: Applications to the restricted three-body problem

Resum: Invariant manifolds in the restricted three-body problem are a powerful tool for the design of spacecraft trajectories. This talk discusses a fully numerical scheme for computing families of quasi-periodic tori and their associated stable and unstable manifolds. A general approach is presented along with examples from the circular and elliptic restricted three-body problems. Including quasi-periodic orbits along with periodic orbits in the design space offers additional low-energy transfer options.

Dia: Dimecres, 25 d'abril de 2012.

Lloc: Aula S05, FME, UPC.

- Hora: 15h45 Café i galetes
- Hora: 16h
- In the first case, the stable and unstable hyperbolic manifolds of the central manifold of L3 play a role in the confinement of trajectories (similarly to what happens for the planar version of the R3BP);
- In the second case, the confinement of trajectories is due to the invariant manifolds of a bi-parametric family of unstable T2 tori associated to a family of periodic orbits that bifurcate from the vertical Lyapunov orbits in the central manifold of L5.

A càrrec de: Priscilla Souza Silva, Universitat de Barcelona

Títol: Domains of Effective Stability near L5 in the R3BP

Resum: It is well known that Effective Stability Domains can occur in non-integrable dynamical systems with N>2 degrees of freedom even when N-dimensional invariant tori are not able to confine trajectories in the 2N phase-space and Arnold diffusion effects are expected.

We are interested in the global shape of the practical stability domains around each triangular equilibrium point of the spatial Restricted Three-body Problem for small values of the mass parameter. Particularly, we want to identify the invariant dynamical structures which account for the long-term confinement of trajectories and are at the boundary of these stability regions.

We present a detailed numerical inspection of the escape processes, identifying two different scenarios:

Dia: Dimecres, 2 de maig de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Marco Antonio Teixeira, UNICAMP Brazil

Títol: Bifurcations in non-smooth planar Dynamical Systems

Resum: The main aim of this talk is to discuss some bifurcations scenario in non-smooth dynamical systems. We present results on the dynamics of some codimension-two and three typical singularities of Filippov planar systems as well as discussion on aspects of the bifurcation diagrams and some dynamical consequences.

Dia: Dimecres, 9 de maig de 2012

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Xavier Jarque, Universitat de Barcelona

Títol: The escaping set for transcendental entire maps

Resum: We will introduce the escaping set, as an invariant subset of the dynamical plane in holomorphic dynamics. We will briefly discuss the case of polynomials (where the escaping set is just the basin of attraction of infinity) and consider the case of entire transcendental maps where the situation is significantly different.

We will present and state some remarkable results of the Eremenko's Conjecture (the connected components of the escaping set are unbounded) and finally we restrict the attention to the complex exponential family to show that for Misiurewicz parameters the escaping set is a connected subset of the complex plane.

Dia: Dimecres, 16 de maig de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Vassili Gelfreykh, University of Warwick

Títol: Arnold Diffusion in a priori chaotic Hamiltonian System

Resum: In this talk we will discuss recent results on generic instability of motion in Hamiltonian systems and symplectic maps in a neighbourhood of an invariant cylinder which posseses a transverse homoclinic connection.

Dia: Dimecres, 23 de maig de 2012

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Erwin Suazo,University of Puerto Rico at Mayaguez

Títol: Transformations on the Study of Evolution Equations

Resum: This presentation is a continuation of my last presentation in March.

This time we will show how some of the results of my last presentation allow us to deduce transformations reducing the study of nonautonomous (with time-dependent coefficients) and inhomogeneous (with space-dependent coefficients) nonlinear Schroedinger equations (NLS) to the standard autonomous nonlinear Schroedinger equation. The latter is a well-known complete integrable system with Lax-Zakharov-Shabat pair, explaining the integrability properties found in the past years for several researchers in nonautonomous and inhomogeneous generalizations of NLS. Similarly we will study these types of transformations for the analogous diffusion-type equation that includes as particular cases the heat, cable, Fokker-Planck and Black-Scholes equation and relates to Burgers-type equation and its traveling wave solutions. Similar results have been found by Konotop et. al. back in 2006. Most of the work presented here is the result of joint work with Sergei K. Suslov

Dia: Dimecres, 6 de juny de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Prof.dr H.W. Broer, University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

Títol: Resonance and fractal geometry

Resum: The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena occur for parameter values in fractal sets of positive measure. We describe a universal phenomenon that plays an important role in modelling. This paper gives a summary of the background theory, veined by examples.

Dia: Dimecres, 13 de juny de 2012

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Prof. Ke Zhang, Department of Mathematics, University of Toronto

Títol: Arnold diffusion via normally hyperbolic cylinders and Mather variational methods

Resum: We discuss an approach to Arnold diffusion combining the geometrical method and Mather's variational method. We use this approach to prove generic Arnold diffusion in two and half degrees of freedom, a theorem announced by J. Mather in 2003. This talk is based on joint works with P. Bernard and V. Kaloshin.

Dia: Dimecres, 20 de juny de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Carles Simó, Universitat de Barcelona

Títol: The stability properties of Hill's linear periodic ODE for large parameters

Resum: The goal is to study the parameter plane in the large for Hill-like
equations, ^{2}cos(ψ), b=ω^{2}sin(ψ)

Dia: Dimecres, 27 de juny de 2012

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Marcel Guàrdia, University of Maryland at College Park

Títol: Growth of Sobolev norms for the cubic defocusing nonlinear Schrödinger equation

Resum: We consider the cubic defocusing nonlinear Schrödinger equation in the
two dimensional torus. Fix *s>1*. Colliander, Keel, Staffilani, Tao and
Takaoka (2010) proved existence of solutions with *s*-Sobolev norm growing
in time by any given factor R. Refining their methods in several aspects
and applying dynamical systems tools, we find solutions with *s*-Sobolev
norm growing in polynomial time in R. This is a joint work with V.
Kaloshin.

Dia: Dimecres, 4 de juliol de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Ariadna Farrés, Observatori de Paris (IMCCE)

Títol: Station Keeping Strategies for Solar Sails

Resum: Solar sails are a new concept of space propulsion that takes advantage of the solar radiation pressure in order to propel a satellite by providing the satellite with a highly reflective area so that the impact and further reflection of the photons emitted by the Sun accelerate the satellite.

Up to the date there have been to successful tests of these technology in space with IKAROS (JAXA) and NanoSail-D2 (NASA). Solar sails open a new range of different mission concepts, such as hovering one of the Earth's poles. In this talk we will review some of these new mission concepts.

We will focus on the station keeping of a solar sail around fixed points and periodic orbits. We will describe the natural dynamics around these objects and use this information to derive station keeping strategies. The variational flow with respect to the sail parameters will help us determine the appropriate changes on the sail orientation to maintain a solar sail close to its nominal orbit.

Dia: Dimecres, 11 de juliol de 2012

Lloc: Aula S05, FME, UPC.

- Hora: 16h Café i galetes
- Hora: 16h15m

A càrrec de: Carlo Danieli, Dipartimento di Matematica, Universita' degli Studi di Padova

Títol: Energy localization in DNA models

Resum: Abstract en PDF

Dia: Dimecres, 18 de juliol de 2012

Lloc: Aula T2 (2n pis), Facultat de Matemàtiques, UB.

- Hora: 16h Café i galetes
- Hora: 16h15m
- Hora: 17h30m Beer seminar

A càrrec de: Amadeu Delshams, UPC.

Títol: Global instability in the elliptic restricted three body problem using two scattering maps

Resum: The goal of this talk is to show the existence of global instability in the elliptic restricted three body problem. The main tool is to combine two different scattering maps associated to the normally parabolic infinity manifold to build trajectories whose angular momentum increases arbitrarily. The computation of such scattering maps will rely heavily on the seminal computations for the circular case initiated first in Jaume Llibre's thesis and finished later on by Llibre and Simo [LlibreS80], which were extended to the elliptic case by Martinez and Pinyol [MartinezP94]. This is a work in progress with Vadim Kaloshin, Abraham de la Rosa and Tere M. Seara.

[LlibreS80] Llibre, Jaume; Simo, Carlos, Oscillatory solutions in the planar restricted three-body problem. Math. Ann. 248 (1980), no. 2, 153-184.

[MartinezP94] Martinez, Regina; Pinyol, Conxita, Parabolic orbits in the elliptic restricted three body problem. J. Differential Equations 111 (1994), no. 2, 299-339.

Last updated: Friday, 14-Sep-2012 15:18:13 CEST