Generic surface homeomorphisms are almost continuum-wise expansive
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917972796243968 |
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| author | Artigue, Alfonso |
| author_facet | Artigue, Alfonso |
| contents | We show that for a compact surface without boundary $M$ the set of cw-expansive homeomorphisms is dense in the set of all the homeomorphisms of $M$ with respect to the $C^0$ topology. After this we show that for a generic homeomorphism $f$ of $M$ it holds that: for all $ε>0$ there is a cw-expansive homeomorphism $g$ of $M$ which is $ε$-close to $f$ and is semiconjugate to $f$; moreover, if $π\colon M\to M$ is this semiconjugacy then $π^{-1}(x)$ is connected, does not separate $M$ and has diameter less than $ε$ for all $x\in M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic surface homeomorphisms are almost continuum-wise expansive Artigue, Alfonso Dynamical Systems We show that for a compact surface without boundary $M$ the set of cw-expansive homeomorphisms is dense in the set of all the homeomorphisms of $M$ with respect to the $C^0$ topology. After this we show that for a generic homeomorphism $f$ of $M$ it holds that: for all $ε>0$ there is a cw-expansive homeomorphism $g$ of $M$ which is $ε$-close to $f$ and is semiconjugate to $f$; moreover, if $π\colon M\to M$ is this semiconjugacy then $π^{-1}(x)$ is connected, does not separate $M$ and has diameter less than $ε$ for all $x\in M$. |
| title | Generic surface homeomorphisms are almost continuum-wise expansive |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.00168 |