Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms

Details Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms

2006-07-12

arxiv.org/abs/math/0607290v1

Discrete and Continuous Dynamical Systems, v. 15, n. 1, p. 225-236, 2006

Mathematics

Dynamical Systems

15 pages

Scientific paper

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.

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