Iteration problem for several chaos in non-autonomous discrete system
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909211349221376 |
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| author | Zeng, Hongbo Huang, Chuangxia Liu, Bingwen |
| author_facet | Zeng, Hongbo Huang, Chuangxia Liu, Bingwen |
| contents | In this paper we investigate the iteration problem for several chaos in non-autonomous discrete system. Firstly, we prove that the Li-Yorke chaos of a non-autonomous discrete dynamical system is preserved under iterations when $f_{1,\infty}$ converges to $f$, which weakens the condition in the literature that $f_{1,\infty}$ uniformly converges to $f$. Besides, we prove that both DC2' and Kato's chaos of a non-autonomous discrete dynamical system are iteration invariants. Additionally, we give a sufficient condition for non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give an example to show that the DC3 of a non-autonomous discrete dynamical system is not inherited under iterations, which partly answers an open question proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems, Appl.Math.Lett. 2013,26:431-436). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Iteration problem for several chaos in non-autonomous discrete system Zeng, Hongbo Huang, Chuangxia Liu, Bingwen Dynamical Systems In this paper we investigate the iteration problem for several chaos in non-autonomous discrete system. Firstly, we prove that the Li-Yorke chaos of a non-autonomous discrete dynamical system is preserved under iterations when $f_{1,\infty}$ converges to $f$, which weakens the condition in the literature that $f_{1,\infty}$ uniformly converges to $f$. Besides, we prove that both DC2' and Kato's chaos of a non-autonomous discrete dynamical system are iteration invariants. Additionally, we give a sufficient condition for non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give an example to show that the DC3 of a non-autonomous discrete dynamical system is not inherited under iterations, which partly answers an open question proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems, Appl.Math.Lett. 2013,26:431-436). |
| title | Iteration problem for several chaos in non-autonomous discrete system |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.17173 |