On the continuity of the SRB entropy for endomorphisms

2004/03/31 by Jose F. Alves, Alves, Jose F., Krerley Oliveira +3
Mathematics · #37C40 #37C75 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C40 #msc:37C75 #msc:37D25

paper · pdf · doi:10.48550/arxiv.math/0403536

19 pages

arxiv created 2004/03/31 · arxiv updated 2009/12/01

Abstract

We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the dynamics. We apply our result to a vast class of non-uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the SRB measure. In particular, we show that the SRB entropy of Viana maps varies continuously with the map.

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