arXiv:2103.12127 Abstract | arXiv Analytics

arXiv:2103.12127 [math.DS]Abstract References Reviews Resources

SRB measures for Anosov actions

Yannick Guedes Bonthonneau, Colin Guillarmou, Tobias Weich

Published 2021-03-22Version 1

Given a general Anosov abelian action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in \cite{BGHW20} using the theory of Ruelle-Taylor resonances. We show that these measures share many properties of Sinai-Ruelle-Bowen measures for general Anosov flows such as smooth desintegrations along the unstable foliation, positive Lebesgue measure basins of attraction and a Bowen formula in terms of periodic orbits.

Comments: 46 pages, 1 figure

Categories: math.DS, math.DG, math.SP

Subjects: 37C40, 37C30, 37D30

Keywords: srb measures, anosov actions, general anosov abelian action, general anosov flows, positive lebesgue measure basins

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