On the continuity of the SRB entropy for endomorphisms
Dynamical Systems
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0403536,
title = {On the continuity of the SRB entropy for endomorphisms},
author = {Jose F. Alves and Krerley Oliveira and Ali Tahzibi},
journal= {arXiv preprint arXiv:math/0403536},
year = {2007}
}
Comments
19 pages