Tel Aviv University Hello everyone, The next colloquium talk will be held on Monday, 16/1/2012, 12:15, Schreiber 006, Tel Aviv University. The speaker is Albert Fathi (ENS Lyon, France) and the title of his talk is Lyapunov Functions: Towards an Aubry-Mather theory for homeomorphisms? The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloqiua, see <http://www.math.tau.ac.il/~klartagb/colloq_2011.html> You are all welcome to suggest colloquium speakers for the second semester, and also for January 30th. Yours, Bo'az ------------- 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. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Bo'az Klartag <klartagb@post.tau.ac.il>