Dia: Dimecres, 18 d'octubre de 2017

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

- Hora: 16h00m Café i galetes
- Hora: 16h15m
A càrrec de: Rodrigo G. Schaefer, Universitat Politécnica de Catalunya

Títol: Scattering maps and global instability in Hamiltonian systems

Resum: In this work we illustrate the Arnold diffusion in a concrete example: the a priori unstable Hamiltonian system of two and a half degrees of freedom:

*H(p,q,𝑰,φ,s) =½p²*+ cos*q*-1 +½𝑰² +*h(q,φ,s;ε),*proving that for any small periodic perturbation of the form

*h(q,φ,s;ε) = ε*cos*q (a₁*cos(*k φ + ls) + a₂*cos*(k'φ + l's ) )**(a₁a₂ ≠ 0, k l'≠ k' l,*and*ε ≠ 0*small enough) there is global instability for the action*𝑰*. For this, we apply a geometrical mechanism based in the explicit computation of several scattering maps.This is a joint work with Amadeu Delshams.

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2009-10 | 2008-09 | 2007-08 | 2006-07 | 2005-06 | 2004-05 | 2003-04 | 2002-03 | 2001-02 | 2000-01 |

1999-00 | 1998-99 | 1997-98 | 1996-97 |

Dia: Dimecres, 27 de setembre de 2017

Lloc: Aula S01, Facultat de Matemàtiques i Estadística, UPC.

- Hora: 16h00m Café i galetes
- Hora: 16h15m
A càrrec de: Tomás Lázaro, Universitat Politécnica de Catalunya

Títol: At the origins of life: small hypercycles with short-circuits

Resum: One of the most challenging open problems in science is to understand the origins of life in Earth primitive state and, in particular, concerning the first primitive replicating systems. Among the existent theories appearing in the last decades, the one conceived by Manfred Eigen and Peter Schuster (1971,1979) states that so-called hypercycles could play a crucial role since they could explain the growth in complexity overcoming the error threshold or critical mutation rate phenomenon. Hypercycles, i.e. nonlinear catalytic networks, allow an all-species coexistence and could support an information content larger than the one found for a quasispecies-based model. This theory received important criticisms due to its high sensitivity to the so-called parasites and short-circuits. While the impact of parasites has been widely investigated for well-mixed and spatial hypercycles, the effect of short-circuits in hypercycles remains poorly understood. In this talk we will present, briefly, a dynamical description of two small asymmetric hypercycles with short-circuits, tackling the question of growing complexity while keeping some stability.

This is a joint work with Ernest Fontich (UB), Toni Guillamon (UPC) and Josep Sardanyés (CRM).

Dia: Dimecres, 25 d'octubre de 2017

Lloc: Aula IMUB (2n pis), Facultat de Matemàtiques i Informàtica, UB.

Afternoon Workshop on "Shilnikov Heritage"

- Hora: 15h50m Registration and welcome coffee
- Hora: 16h00m
A càrrec de: Sergey Gonchenko, Institute for Applied Mathematics and Cybernetics, N. Novgorod, Russia

Títol: Shilnikov heritage: review of his classical and pioneering works

Resum: I will try to fulfil an impossible task: to give a more or less intelligible overview of the pioneer classical L.P.Shilnikov works of 60-80th years. The main Shilnikov results obtained in this period can be grouped into 5 main topics:

- bifurcations of separatrix loop in multidimensional systems;
- homoclinic loop of a saddle-focus and mathematical theory of spiral chaos;
- homoclinic chaos;
- mathematical theory of synchronization, and chaos;
- Lorenz attractor.

- Hora: 17h00m Coffee Break
- Hora: 17h25m
A càrrec de: Dmitry Turaev, Imperial College, UK.

Títol: A positive metric entropy conjecture

Resum: We prove that any area-preserving diffeomorphism with an elliptic periodic point can be perturbed, in C-infinity topology, to one exhibiting a chaotic island with positive metric entropy (a joint work with P.Berger)

Sessió actual.

Last updated: Monday, 20-Nov-2017 08:39:51 CET