Non-robustly intermingled basins for perturbations of time-one map of Anosov flows

2016/01/30 by Qianying Xiao, Xiao, Qianying, Zuohuan Zheng +1
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis #math.DS

paper · pdf · doi:10.48550/arxiv.1602.00080

9 pages

arxiv created 2016/01/30 · openalex publication_date 2016/01/30 · arxiv updated 2016/02/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Perturbations of time-one maps of transitive Anosov flows are studied. We show that most perturbations have no intermingled basins of hyperbolic physical measures.

Related

• On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics
• A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows
• Global stability of discretized Anosov flows
• Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map
• On the rate of mixing of circle extensions of Anosov maps