CRM: Centro De Giorgi
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Inaugural Conference of the Fibonacci Laboratory

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

speaker: Albert Fathi (Georgia Institute of Technology)

abstract: This is a joint work with Pierre Pageault.
 For a 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 Mañé potential in Lagrangian systems. By analogy to Mather's theory of Lagrangian Systems we will produce an Aubry set which is the generalized recurrence set introduced in the 60's by Joe Auslander (via transfinite induction) and a Mañé set which is essentially Conley's chain recurrent set.
 The level of the lecture will be elementary (nothing beyond topology of metric spaces and calculus of one variable ).

Mon 5 Mar, 17:00 - 18:00, Sala Azzurra
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