Completely Li--Yorke chaotic homeomorphisms with positive entropy
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913533939154944 |
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| author | Lin, Zijie Ye, Xiangdong |
| author_facet | Lin, Zijie Ye, Xiangdong |
| contents | It is an open problem whether a homeomorphism on a compact metric space satisfying that each proper pair is either positively or negatively Li--Yorke, called completely Li--Yorke chaotic, can have positive entropy. In the present paper, an affirmative answer to this question is given. In fact, for each homeomorphism $T$ with positive entropy such that each proper pair is not two-sided asymptotic, a completely Li--Yorke chaotic homeomorphism with positive entropy associated with the given homeomorphism can be constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completely Li--Yorke chaotic homeomorphisms with positive entropy Lin, Zijie Ye, Xiangdong Dynamical Systems It is an open problem whether a homeomorphism on a compact metric space satisfying that each proper pair is either positively or negatively Li--Yorke, called completely Li--Yorke chaotic, can have positive entropy. In the present paper, an affirmative answer to this question is given. In fact, for each homeomorphism $T$ with positive entropy such that each proper pair is not two-sided asymptotic, a completely Li--Yorke chaotic homeomorphism with positive entropy associated with the given homeomorphism can be constructed. |
| title | Completely Li--Yorke chaotic homeomorphisms with positive entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.04069 |