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April  2007, 17(2): 371-386. doi: 10.3934/dcds.2007.17.371

Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures

Vítor Araújo 1,

1. 

Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21.945-970 Rio de Janeiro, RJ, Brazil

Received  December 2005 Revised  September 2006 Published  November 2006

We obtain results on existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, deducing sufficient conditions for continuity of physical measures and, for local diffeomorphisms, necessary and sufficient conditions for stochastic stability. In particular we show that, under certain conditions, stochastically robust non-uniform expansion implies existence and continuous variation of physical measures.
Keywords: equilibrium states; physical measures; statistical stability; stochastic stability; uniform random generating partitions..
Mathematics Subject Classification: Primary: 37D25; Secondary: 37D3.
Citation: Vítor Araújo. Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 371-386. doi: 10.3934/dcds.2007.17.371
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