Li-Yorke chaos for maps on G-Spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916377825116160 |
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| author | Zhao, Yingcui |
| author_facet | Zhao, Yingcui |
| contents | We introduce the definition of Li-Yorke chaos for the map f on G-spaces, and show G-Li-Yorke chaos is iterable for f. Li-Yorke chaos implies G-Li-Yorke chaos, while the converse is not true. Then we give a sufficient condition for f to be chaotic in the sense of G-Li-Yorke. Also, we prove that if f is G-transitive and there exists a common fixed point for f and all of the maps in G, then f is chaotic in the sense of G-Li-Yorke. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07944 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Li-Yorke chaos for maps on G-Spaces Zhao, Yingcui Dynamical Systems We introduce the definition of Li-Yorke chaos for the map f on G-spaces, and show G-Li-Yorke chaos is iterable for f. Li-Yorke chaos implies G-Li-Yorke chaos, while the converse is not true. Then we give a sufficient condition for f to be chaotic in the sense of G-Li-Yorke. Also, we prove that if f is G-transitive and there exists a common fixed point for f and all of the maps in G, then f is chaotic in the sense of G-Li-Yorke. |
| title | Li-Yorke chaos for maps on G-Spaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2210.07944 |