Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915701433827328 |
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| author | Sarmiento, Alberto Danton, Douglas Valério, Viviane Pardini |
| author_facet | Sarmiento, Alberto Danton, Douglas Valério, Viviane Pardini |
| contents | In this paper, we construct cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected. This provides an affirmative answer to question posed by Artigue [3]. To achieve this, we generalize the construction from the example of Artigue, Pacifico and Vieitez [6], obtaining examples of homeomorphisms on compact surfaces of genus greater than or equal to two that are 2-expansive but not expansive. On the sphere and the torus, we construct new examples of cw2-expansive homeomorphisms that are not N -expansive for all N greater than or equal to one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus Sarmiento, Alberto Danton, Douglas Valério, Viviane Pardini Dynamical Systems 37C70, 37B20 In this paper, we construct cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected. This provides an affirmative answer to question posed by Artigue [3]. To achieve this, we generalize the construction from the example of Artigue, Pacifico and Vieitez [6], obtaining examples of homeomorphisms on compact surfaces of genus greater than or equal to two that are 2-expansive but not expansive. On the sphere and the torus, we construct new examples of cw2-expansive homeomorphisms that are not N -expansive for all N greater than or equal to one. |
| title | Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus |
| topic | Dynamical Systems 37C70, 37B20 |
| url | https://arxiv.org/abs/2512.24904 |