Anosov actions: minimality of foliations or suspension action

2025/05/30 by Lopes, Rodrigo R., Maquera, Carlos, Varão, Régis
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.24598

Abstract

We prove that an Anosov action of 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 ℤ^k-Anosov action. This represents an important progress toward addressing Verjovsky's extended conjecture for Anosov actions, as developed by Barbot and Maquera.

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