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

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February 2006, 15(1): 225-236. doi: 10.3934/dcds.2006.15.225

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

Krerley Oliveira ^1, and Marcelo Viana ^2,

1.	Departamento de Matemática - UFAL, Campus A.C. Simões, s/n 57072-090 Maceió, Alagoas, Brazil
2.	IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ

Received September 2004 Revised February 2005 Published February 2006

Abstract
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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: Entropy, maximizing measure, non-uniform hyperbolicity..

Mathematics Subject Classification: Primary: 37D25, 37D35, 37A35; Secondary: 37A6.

Citation: Krerley Oliveira, Marcelo Viana. Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 225-236. doi: 10.3934/dcds.2006.15.225

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