Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms
Dynamical Systems
2007-05-23 v1
Abstract
We prove existence of maximal entropy measures for an open set of non-uniformly expanding local diffeomorphisms on a compact Riemannian manifold. In this context the topological entropy coincides with the logarithm of the degree, and these maximizing measures are eigenmeasures of the transfer operator. When the map is topologically mixing, the maximizing measure is unique and positive on every open set.
Keywords
Cite
@article{arxiv.math/0607290,
title = {Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms},
author = {Krerley Oliveira and Marcelo Viana},
journal= {arXiv preprint arXiv:math/0607290},
year = {2007}
}
Comments
15 pages