Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.
A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.
Food and drinks are served after the event, usually in Espace 7!
Date: Tuesday, June 3rd 2025 (15:30-16:30, room A709)
Speaker: (Università di Roma "Tor Vergata")
Title: Recursive behaviors of Hamiltonian dynamical systems in finite and infinite dimension
Abstract: Nonlinear dynamical systems both in finite and infinite dimension are a fundamental instrument to understand/modelize physical phenomena, which often have recursive/undulatory nature: the rotation of a satellite, the behavior of a planetary system, the motion of the sea, the deflection of a beam, electromagnetic waves (light, radio waves)... Many of these are modeled by Hamiltonian differential equations (ODEs in finite dimension or PDEs in the infinite case) and their mathematical description is often extremely complicated, characte- rized by a non-trivial interplay between stable and chaotic behaviors. A paradigmatic approach consists in studying the existence, stability, robustness and genericity of invariant manifolds that support a global dynamics which can be explicitly described. In the nearly integrable finite dimensional case, these objects are typically tori, have almost full measure, and support a Kronecker flow; this is a rather well established subject. In the infinite dimensional setting, very little is known and the results that one can obtain are strongly related to the boundary conditions of the PDE at stake. In this talk I shall give an overview of this fascinating subject and focus on some specific results regarding the existence of solutions and long time stability.