PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Title:Lyapunov Functions: Towards an Aubry-Mather theory for homeomorphisms?
Seminar:Department of Mathematics Colloquium
Speaker:Albert Fathi, ENS de Lyon, France
Abstract:
This is a joint work with Ettore Minguzzi and Pierre Pageault. For an homeomorphism h of a compact space, a Lyapunov function a 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.

Room Reservation Information

Room Number:MB114
Date:03 / 24 / 2011
Time:04:00pm - 05:00pm