2025/02/27 by Benjamin Delarue, Delarue, Benjamin, Daniel Monclair +3 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Cellular Automata and Applications #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2502.20195
openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a non-compact semisimple real Lie group G and an Anosov subgroup Γ, we utilize the correspondence between \mathbb R-valued additive characters on Levi subgroups L of G and \mathbb R-affine homogeneous line bundles over G/L to systematically construct families of non-empty domains of proper discontinuity for the Γ-action. If Γ is torsion-free, the analytic dynamical systems on the quotients are Axiom A, and assemble into a single partially hyperbolic multiflow. Each Axiom A system admits global analytic stable/unstable foliations with non-wandering set a single basic set on which the flow is conjugate to Sambarino's refraction flow, establishing that all refraction flows arise in this fashion. Furthermore, the \mathbb R-valued additive character is regular if and only if the associated Axiom A system admits a compatible pseudo-Riemannian metric and contact structure, which we relate to the Poisson structure on the dual of the Lie algebra of G.