Dia: Dimecres 4 de juny de 2025
Lloc: Aula S01, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Bhanu Kumar, University of Michigan
Títol: Mean motion resonant phenomena, orbits, and transfers in planet-moon systems
Resum: In this talk, I will discuss resonant orbits and the phenomenon of mean-motion resonance overlapping, which generate natural heteroclinic, propellant-free pathways that spacecraft can follow to change their semimajor axis. This is useful for low-fuel and/or low-energy space mission trajectory design. I will start by describing some recent related results from the Earth-Moon system, with applications to missions throughout cislunar space. Then, moving to the more complicated systems of the outer planets, which have multiple moons, I will discuss secondary resonant phenomena which occur inside the normally hyperbolic invariant manifolds formed by unstable mean motion resonant orbit families. The secondary resonances inside these manifolds are found to overlap in some cases, resulting in a total change of structure for the more unstable members of such families - precisely the orbits most useful for outer planet tour design.
A càrrec de: Marian Gidea, Yeshiva University
Títol: Diffusion in Hamiltonian systems driven by random perturbations
Resum: The main idea of the present work is using randomness to overcome geometric obstacles in dynamical systems. We consider a pendulum-rotator system driven by a stochastic process. We show that for almost every realization of the stochastic process, there is a distinguished set of times for which there exists a random normally hyperbolic invariant manifold. We also show that there are transverse intersections of the stable and unstable manifolds, which are given by the non-degenerate zeroes of a Melnikov stochastic process. We obtain the existence of orbits along which the energy changes over time. This is based on joint work with A-M Cherubini.
Last updated: Tue Jun 17 11:17:07 2025