Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911315824476160 |
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| author | Lanneau, Erwan Liechti, Livio Tsang, Chi Cheuk |
| author_facet | Lanneau, Erwan Liechti, Livio Tsang, Chi Cheuk |
| contents | We show that the stretch factor $λ(f)$ of an orientation-reversing fully-punctured pseudo-Anosov map $f$ on a finite-type orientable surface $S$, with $-χ(S) \geq 4$ and having at least two puncture orbits, satisfies the inequality $λ(f)^{-χ(S)} \geq σ^2$, where $σ=1+\sqrt{2}$ is the silver ratio. We provide examples showing that this bound is asymptotically sharp. This extends previous results of Hironaka and the third author to orientation-reversing maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps Lanneau, Erwan Liechti, Livio Tsang, Chi Cheuk Geometric Topology Dynamical Systems We show that the stretch factor $λ(f)$ of an orientation-reversing fully-punctured pseudo-Anosov map $f$ on a finite-type orientable surface $S$, with $-χ(S) \geq 4$ and having at least two puncture orbits, satisfies the inequality $λ(f)^{-χ(S)} \geq σ^2$, where $σ=1+\sqrt{2}$ is the silver ratio. We provide examples showing that this bound is asymptotically sharp. This extends previous results of Hironaka and the third author to orientation-reversing maps. |
| title | Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2402.15369 |