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

Krerley Oliveira; Marcelo Viana

doi:10.3934/dcds.2006.15.225

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2006, Volume 15, Issue 1: 225-236. Doi: 10.3934/dcds.2006.15.225

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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
2.
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ

Received: August 31, 2004

Revised: January 31, 2005

Published: February 2006

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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.

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Mathematics Subject Classification: Primary: 37D25, 37D35, 37A35; Secondary: 37A60.

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