On the continuity of the SRB entropy for endomorphisms

Details On the continuity of the SRB entropy for endomorphisms On the continuity of the SRB entropy for endomorphisms

2004-03-31

arxiv.org/abs/math/0403536v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

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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