Conformally symplectic dynamics
Ponente: Marie-Claude Arnaud (Université Paris-Cité)Fecha: viernes 31 de marzo de 2023 - 10:30 - 13:00Lugar: Aula Naranja, ICMAT
Hamiltonian and symplectic dynamics, that are defined on a symplectic manifold and preserve the symplectic form, have been widely studied. They concentrate many recurrence phenomena. Conformal symplectic dynamics change the symplectic form up to a multiplicative factor and in this setting, dissipative behaviors may happen (as the existence of attractors). In the first lecture, using viewpoints of dynamical systems and symplectic topology, I will introduce these dynamics and describe some general results concerning their invariant sets (invariant submanifolds, attractors…). In the second lecture, I will introduce the so-called discounted Hamilton-Jacobi partial differential equation, give a dynamical interpretation of it and make the link between the solution of this PDE and the concept introduced in the first lecture. Some results are joint works with Fejoz, Humilière and Viterbo.
10:30 - 11:30. Lecture 1
11:30 - 12:00. Break
12:00 - 13:00. Lecture 2