Ping-pong dynamics of hyperbolic-like actions with non-simple points

2025/06/02 by K.H. Kim, Kim, KyeongRo, Michele Triestino +1
Mathematics · Physics and Astronomy · #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Primary: 57M60 #Quantum chaos and dynamical systems #Secondary: 37C85 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2506.01690

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A hyperbolic-like group is a subgroup of Homeo₊(S¹) such that every non-trivial element has exactly two fixed points, one attracting and one repelling. We investigate the ping-pong dynamics of hyperbolic-like groups, inspired by a conjecture of Bonatti. We show the existence of a proper ping-pong partition for any pair of non-cyclic point stabilizers. More precisely, our results explicitly provide such a ping-pong partition.

Citations

• Non-locally discrete actions on the circle with at most N fixed points
• Coarse hyperbolicity and closed orbits for quasigeodesic flows

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