SRB MEASURES FOR ANOSOV ACTIONS

Yannick Guedes Bonthonneau (1) , Colin Guillarmou (2) , Tobias Weich (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LMO - Laboratoire de Mathématiques d'Orsay
3 UPB - Universität Paderborn

Given a general Anosov R κ action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in [GBGHW20] 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.

Domaines: Mathématiques [math]

Yannick Guedes Bonthonneau, Colin Guillarmou, Tobias Weich. SRB MEASURES FOR ANOSOV ACTIONS. Journal of Differential Geometry, In press. ⟨hal-03325073v3⟩