PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Some results about equilibrium measures for non-uniformly expanding maps
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Krerley Oliveira (Universidade Federal de Alagoas)
Abstract:
In this talk we address ourselfs to some recent results (joint with M. Viana) about existence, uniqueness and some ergodic properties of equilibrium measures for local diffeomorphisms exibting non-uniform expanding behaviour. Two main results will be discussed: a) Existence and uniqueness of maximal entropy measures; b) Uniqueness of equilibrium measures for H\"older continuous potentials not too far from constant. In this last case, we develop a Ruelle-Perron-Fr\"obenius transfer operator approach to the ergodic theory of a large class of non-uniformly expanding transformations on compact manifolds. We prove that the transfer operator has a positive eigenfunction, piecewise H\"older continuous, and use this fact to show that there is exactly one equilibrium state. Moreover, the equilibrium state is a non-lacunary Gibbs measure, a non-uniform version of the classical notion of Gibbs measure. Time permiting, we discuss some very recent extensions of these results for diffeomorphisms.

Room Reservation Information

Room Number:MB106
Date:09 / 24 / 2007
Time:03:35pm - 05:40pm