Tangent bundles to regular basic sets in hyperbolic dynamics

2010/09/01 by Luchezar Stoyanov, Stoyanov, Luchezar
Mathematics · Physics and Astronomy · #37D20 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37D20 #msc:37D40

paper · pdf · doi:10.48550/arxiv.1009.0102

7 pages

arxiv created 2010/09/01 · openalex publication_date 2010/09/01 · arxiv updated 2010/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a locally maximal compact invariant hyperbolic set Λ for a C¹ flow or diffeomorphism on a Riemann manifold with C¹ unstable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable manifolds that locally approximates Λ in a certain way.

Related

• Persistent bundles over a two dimensional compact set
• Partially Hyperbolic Sets with a Dynamically Minimal Invariant Lamination
• Nonlocally maximal and premaximal hyperbolic sets
• Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation
• Integrability of Continuous Bundles