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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17193 |
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| _version_ | 1866915460348379136 |
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| author | Agarwal, Nikita Mahure, Rohan Suresh Rajeevsarathy, Kashyap |
| author_facet | Agarwal, Nikita Mahure, Rohan Suresh Rajeevsarathy, Kashyap |
| contents | Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\mathrm{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\to S_g$ be the regular infinite-sheeted cover with deck transformation group $\mathbb{Z}$. In this paper, we show the existence of ``pseudo-Anosov-like'' maps on $\mathcal{L}$ that arise as the lifts of Penner-type pseudo-Anosov maps on $S_g$ under the cover $q_g$. Furthermore, we establish that these lifts are topologically transitive, mixing, and support null recurrent dynamics. Moreover, we present concrete examples of infinite families of such maps on $\mathcal{L}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a family of pseudo-Anosov-like maps on the infinite ladder surface Agarwal, Nikita Mahure, Rohan Suresh Rajeevsarathy, Kashyap Geometric Topology Dynamical Systems Probability Primary: 37A05, 57K20, Secondary: 37A05, 37A40, 37B10 Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\mathrm{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\to S_g$ be the regular infinite-sheeted cover with deck transformation group $\mathbb{Z}$. In this paper, we show the existence of ``pseudo-Anosov-like'' maps on $\mathcal{L}$ that arise as the lifts of Penner-type pseudo-Anosov maps on $S_g$ under the cover $q_g$. Furthermore, we establish that these lifts are topologically transitive, mixing, and support null recurrent dynamics. Moreover, we present concrete examples of infinite families of such maps on $\mathcal{L}$. |
| title | On a family of pseudo-Anosov-like maps on the infinite ladder surface |
| topic | Geometric Topology Dynamical Systems Probability Primary: 37A05, 57K20, Secondary: 37A05, 37A40, 37B10 |
| url | https://arxiv.org/abs/2508.17193 |