Rigidity of U-Gibbs measures near conservative Anosov diffeomorphisms on \mathbbT³

2022/07/30 by Sébastien Alvarez, Alvarez, Sébastien, Martin Leguil +5
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2208.00126

openalex publication_date 2022/07/30 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We show that within a C¹-neighbourhood U of the set of volume preserving Anosov diffeomorphisms on the three-torus \mathbbT³ which are strongly partially hyperbolic with expanding center, any f\inU\capDiff²(\mathbbT³) satisfies the dichotomy: either the strong stable and unstable bundles E^s and E^u of f are jointly integrable, or any fully supported u-Gibbs measure of f is SRB.

Citations

• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Invariant measures for higher-rank hyperbolic abelian actions
• Normal forms on contracting foliations: smoothness and homogeneous structure
• Finiteness of partially hyperbolic attractors with one-dimensional\n center
• Geometric properties of partially hyperbolic measures and applications to measure rigidity

Related

• A numerical study of Gibbs u-measures for partially hyperbolic diffeomorphisms on \mathbb T³
• A Note on Rigidity of Anosov diffeomorphisms of the Three Torus
• Rigidity of center Lyapunov exponents for Anosov diffeomorphisms on 3-torus
• Entropy rigidity of u-Gibbs measures
• Rigidity of center Lyapunov exponents and su-integrability