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On the continuity of the SRB entropy for endomorphisms

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arxiv math/0403536 v1 pith:N3H3SLAW submitted 2004-03-31 math.DS

Jose F. Alves , Krerley Oliveira , Ali Tahzibi This is my paper · ORCID
classification math.DS
keywords entropymapscontinuitycontinuouslymeasureparticularprovevaries
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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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