Anosov actions: Minimality of foliations or suspension action
Abstract
We prove that an Anosov action of $\mathbb{R}^k$ over a compact manifold $M$ transitive on regular sub-cones satisfies the dichotomy: each stable and unstable leaf is dense or the Anosov action is topologically conjugated to a suspension of a $\mathbb{Z}^k$-Anosov action. This represents an important progress toward addressing Verjovsky's extended conjecture for Anosov actions, as developed by Barbot and Maquera.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 30 July 2026
- Language
- EN