Smooth rigidity for 3-dimensional volume preserving Anosov flows and weighted marked length spectrum rigidity

2022/10/05 by Andrey Gogolev, Federico Rodriguez Hertz, Gogolev, Andrey +1 · 2 citations
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.02295

openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X₁^t and X₂^t be volume preserving Anosov flows on a 3-dimensional manifold M. We prove that if X₁^t and X₂^t are C⁰ conjugate then the conjugacy is, in fact, smooth, unless M is a mapping torus of an Anosov automorphism of \mathbb T² and both flows are constant roof suspension flows. We deduce several applications. Among them is a new result on rigidity of Anosov diffeorphisms on \mathbb T² and a new "weighted" marked length spectrum rigidity result for surfaces of negative curvature.

Cited by

• Rigidity of the unstable foliation
• Marked Poincaré rigidity near hyperbolic metrics and injectivity of the Lichnerowicz Laplacian in dimension 3

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