Periodic points of endperiodic maps
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912182229270528 |
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| author | Buckminster, Ellis |
| author_facet | Buckminster, Ellis |
| contents | Let $g\colon L\rightarrow L$ be an atoroidal, endperiodic map on an infinite type surface $L$ with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, $g$ is isotopic to a spun pseudo-Anosov map $f$. We show that spun pseudo-Anosov maps minimize the number of periodic points of period $n$ for sufficiently high $n$ over all maps in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor. We also show that the same theorem holds for atoroidal Handel--Miller maps when one only considers periodic points that lie in the intersection of the stable and unstable laminations. Furthermore, we show via example that spun-pseudo Anosov and Handel--Miller maps do not always minimize the number of periodic points of low period. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic points of endperiodic maps Buckminster, Ellis Dynamical Systems Geometric Topology Let $g\colon L\rightarrow L$ be an atoroidal, endperiodic map on an infinite type surface $L$ with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, $g$ is isotopic to a spun pseudo-Anosov map $f$. We show that spun pseudo-Anosov maps minimize the number of periodic points of period $n$ for sufficiently high $n$ over all maps in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor. We also show that the same theorem holds for atoroidal Handel--Miller maps when one only considers periodic points that lie in the intersection of the stable and unstable laminations. Furthermore, we show via example that spun-pseudo Anosov and Handel--Miller maps do not always minimize the number of periodic points of low period. |
| title | Periodic points of endperiodic maps |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2409.05963 |