Accessibility and ergodicity of partially hyperbolic diffeomorphisms without periodic points
Abstract
We prove that every $ C^2 $ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz–Hertz–Ures [60] in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold $ M $ with no periodic points is accessible if the non-wandering set is all of $ M $ and the fundamental group $ \pi_1(M) $ is not virtually solvable.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Journal of Modern Dynamics
- Volume
- 22
- Issue
- 0
- Pages
- 643–694
- Publication date
- 1 January 2026
- Language
- EN