Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929591876059136 |
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| author | Jiang, Zhen Li, Jian |
| author_facet | Jiang, Zhen Li, Jian |
| contents | Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of completely metrizable groups, and characterize three kinds of chaos (resp. extreme chaos) in terms of the existence of the so-called semi-irregular points (resp. irregular points). We exhibit some examples of inner automorphisms of Polish groups to illustrate the results. We also apply our results to the chaos theory of continuous linear operators on Fréchet spaces, which improves some results in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06304 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces Jiang, Zhen Li, Jian Dynamical Systems Functional Analysis 47A16, 37B05 Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of completely metrizable groups, and characterize three kinds of chaos (resp. extreme chaos) in terms of the existence of the so-called semi-irregular points (resp. irregular points). We exhibit some examples of inner automorphisms of Polish groups to illustrate the results. We also apply our results to the chaos theory of continuous linear operators on Fréchet spaces, which improves some results in the literature. |
| title | Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces |
| topic | Dynamical Systems Functional Analysis 47A16, 37B05 |
| url | https://arxiv.org/abs/2212.06304 |