On zero entropy homeomorphisms of the pseudo-arc
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909310505713664 |
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| author | Činč, Jernej |
| author_facet | Činč, Jernej |
| contents | In this paper we study interval maps $f$ with zero topological entropy that are crooked; i.e. whose inverse limit with $f$ as the single bonding map is the pseudo-arc. We show that there are uncountably many pairwise non-conjugate zero entropy crooked interval maps with different sets of fixed points. We also show that there are uncountably many zero entropy crooked maps that are pairwise non-conjugate and have exactly two fixed points. Furthermore, we provide a characterization of crooked interval maps that are under or above the identity diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On zero entropy homeomorphisms of the pseudo-arc Činč, Jernej Dynamical Systems General Topology 37E05, 37B45 In this paper we study interval maps $f$ with zero topological entropy that are crooked; i.e. whose inverse limit with $f$ as the single bonding map is the pseudo-arc. We show that there are uncountably many pairwise non-conjugate zero entropy crooked interval maps with different sets of fixed points. We also show that there are uncountably many zero entropy crooked maps that are pairwise non-conjugate and have exactly two fixed points. Furthermore, we provide a characterization of crooked interval maps that are under or above the identity diagonal. |
| title | On zero entropy homeomorphisms of the pseudo-arc |
| topic | Dynamical Systems General Topology 37E05, 37B45 |
| url | https://arxiv.org/abs/2405.20533 |