Infinitely many homeomorphic hyperbolic plugs with the same basic sets

Chen, Fangfang

doi:10.2140/agt.2025.25.4147

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Infinitely many homeomorphic hyperbolic plugs with the same basic sets

Fangfang Chen

Algebraic & Geometric Topology 25 (2025) 4147–4161

DOI: 10.2140/agt.2025.25.4147

Abstract

Using Ghys’ work on the geodesic flow of the modular surface, we construct infinitely many smooth flows on $T^{2} \times [0, 1]$ transverse to the boundary, whose maximal invariant sets are the same saddle hyperbolic set, but whose global dynamics are not topologically equivalent pairwise. As a corollary of the previous construction, we prove that there exist infinitely many simple Smale flows on $S^{3}$ with the same basic sets but different global dynamics.

Keywords

hyperbolic plugs, geodesic flows, simple Smale flows

Mathematical Subject Classification

Primary: 37D40, 37D45

References

Publication

Received: 4 January 2024

Revised: 15 September 2024

Accepted: 2 November 2024

Published: 29 October 2025

Authors

Fangfang Chen
School of Mathematical Sciences Tongji University Shanghai China	School of Mathematics and Statistics Huangshan University Huangshan China

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Volume 25, issue 7 (2025)