Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, January 16, 2012

Schreiber 006, 12:15

Albertt Fathi

ENS Lyon, France

Lyapunov Functions: Towards an Aubry-Mather theory for homeomorphisms?

Abstract: This is a joint work with Pierre Pageault. For a homeomorphism h of a compact space, a Lyapunov function is a real valued function that is non-increasing along orbits for h. By looking at simple dynamical systems (=homeomorphisms) on the circle, we will see that there are systems which are topologically conjugate and have Lyapunov functions with various regularity. This will lead us to define barriers analogous to the well known Peierls barrier or to the Mane potential in Lagrangian systems. That will produce by analogy to Mather's theory of Lagrangian Systems an Aubry set which is the generalized recurrence set introduced in the 60's by Joe Auslander (via transfinite induction) and a Mane set which is essentially Conley's chain recurrent set.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006