SRB measures for Anosov actions

2021/03/22 by Bonthonneau, Yannick Guedes, Guillarmou, Colin, Weich, Tobias · 1 citation
#37C30 #37C40 #37D30 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2103.12127

Abstract

Given a general Anosov ℝ^κ action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in \citeBGHW20 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.

Cited by

• Unstable entropy for Anosov diffeomorphisms on the 3-torus

Related

• Ruelle-Taylor resonances of Anosov actions
• Unique SRB measures and transitivity for Anosov diffeomorphisms
• Measure of maximal entropy for minimal Anosov actions
• Horospherical invariant measures and a rank dichotomy for Anosov groups
• Anosov actions: minimality of foliations or suspension action