Emergence of wild dynamics

Pierre Berger, CNRS-IMJ-PRG
Fine Hall 314

In-Person and Online Talk

Zoom Link:  https://princeton.zoom.us/j/99250301045

Passcode required.

In dynamical systems, a main question is the description of the asymptotic and statistical behaviors of most of the orbits for a typical system. The quasi-periodic and chaos theories provide many examples of ergodic systems: a.e. orbit is equi-distributed following the same law.

We will present examples of dynamics which are wild in the sense that their statistical behavior is extremely complicated; in particular they display infinitely many simultaneous statistical behaviors. We will discuss the typicality of such systems and how to understand them. The presented results will be in many settings: dissipative dynamics, symplectic dynamics, complex dynamics or steady Euler flow.