Functional Poisson approximations for some dissipative systems

CDSNS Colloquium
Friday, September 30, 2022 - 3:30pm for 1 hour (actually 50 minutes)
In-person in Skiles 006
Yaofeng Su – Georgia Tech –
Alex Blumenthal

The study of Poisson approximations of the process of recurrences to small subsets in the phase spaces of chaotic dynamical systems, started in 1991, have developed by now into a large active area of the dynamical systems theory. In this talk, I will present some new results. This is a joint work with Prof. Leonid Bunimovich.

  1. I will start with some examples of dissipative hyperbolic systems,
  2. then formulate the question of functional Poisson approximations for these systems.
  3. To study Poisson approximations, I will present two difficulties, called short returns and ring conditions.
  4. These two difficulties can be partially solved under some conditions of, e.g. the dimension of the dynamics, the Hausdorff dimension of the SRB measure, etc. I will present a new method which does not depend on dimensions but can completely solve these two difficulties for dissipative systems.