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SRB measures for Anosov actions by Bonthonneau, Yannick Guedes; Guillarmou, Colin; Weich, Tobias is a scholarly article available to read on EtoBox.

What is SRB measures for Anosov actions about?

Given a general Anosov $\mathbb{R}^\kappa$ 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 disintegrations along the unstable foliation, positive Lebesgue measure basins of attraction and a Bowen formula in terms of periodic orbits. Finally we show that if the action in the positive Weyl chamber is transitive, the measure is unique and has full support.

Author

Bonthonneau, Yannick Guedes; Guillarmou, Colin; Weich, Tobias

Published

2021

Language

EN