Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

2018/09/07 by Sérgio R. Fenley, Fenley, Sergio, Rafaël Potrie +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1809.02284

openalex publication_date 2018/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conservative partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. We show that they are always accessible and deduce as a result that every conservative C¹⁺ partially hyperbolic in a hyperbolic 3-manifold must be ergodic, giving an afirmative answer to a conjecture of Hertz-Hertz-Ures in the context of hyperbolic 3-manifolds. Some of the intermediary steps are also done for general partially hyperbolic diffeomorphisms homotopic to the identity.

Related

• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three
• Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points
• Partial hyperbolicity and ergodicity in dimension three
• Ergodicity and partial hyperbolicity on Seifert manifolds
• Partially hyperbolic diffeomorphisms homotopic to the identity on\n 3-manifolds