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

KyeongRo Kim; Michele Triestino

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arXiv · 2506.01690

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

KyeongRo Kim·Michele Triestino

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Abstract

A hyperbolic-like group is a subgroup of $\operatorname{Homeo}_+(S^1)$ 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.

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BibTeX RIS

KyeongRo Kim, Michele Triestino. 2025-06-02. Ping-pong dynamics of hyperbolic-like actions with non-simple points. https://arxiv.org/abs/2506.01690

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