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)
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