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Seminar in Mathematical Physics: “Invariant sets of some dissipative systems”

Wednesday, September 18, 2019, h. 14:30 - Room 2BC60 - Stefano Marò

ARGOMENTI: Seminars

Wednesday, September 18, 2019, h. 14:30
Room 2BC60
Stefano Marò (Pisa)
“Invariant sets of some dissipative systems”

Abstract
We study the dynamics and the invariant sets for a class of dissipative systems, namely conformally symplectic systems. More precisley, we consider flows that do not preserve the symplectic structure but do alter it up to a constant scalar factor. The study of invariant Lagrangian submanifolds for these systems, in particular KAM tori, has been investigated by means of varied techniques in recent years. We will focus on what happens when these invariant Lagrangian submanifolds stop to exist. Inspired by the celebrated Aubry-Mather and Weak KAM theories for Hamiltonian systems, we prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. We describe the structure and the dynamical significance of these sets, their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.