On stable transitivity of finitely generated groups of volume preserving diffeomorphisms

2017/01/19 by Zhiyuan Zhang, Zhang, Zhiyuan
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1701.05272

openalex publication_date 2017/01/19 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide a new criterion for the stable transitivity of volume preserving finite generated group on any compact Riemannian manifold. As one of our applications, we generalised a result of Dolgopyat and Krikorian in \citeDK and obtained stable transitivity for random rotations on the sphere in any dimension. As another application, we showed that for ∞ ≥ r ≥ 2, any C^r volume preserving partially hyperbolic diffeomorphism g on any compact Riemannian manifold M having sufficiently Hölder stable or unstable distribution, for any sufficiently large integer K, for any (f_i)_i=1^K in a C¹ open C^r dense subset of \textnormal\Diff^r(M,m)^K, the group generated by g, f₁,⋯, f_K acts transitively.

Citations

• Extremal Lyapunov exponents: an invariance principle and applications

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