On several dynamical properties of shifts acting on directed trees
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914365877256192 |
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| author | Abakumov, Evgeny Abbar, Arafat |
| author_facet | Abakumov, Evgeny Abbar, Arafat |
| contents | This paper explores the notions of $\mathcal{F}$-transitivity and topological $\mathcal{F}$-recurrence for backward shift operators on weighted $\ell^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal{F}$ represents a Furstenberg family of subsets of $\mathbb{N}_0$. In particular, we establish the equivalence between recurrence and hypercyclicity of these operators on unrooted directed trees. For rooted directed trees, a backward shift operator is hypercyclic if and only if it possesses an orbit of a bounded subset that is weakly dense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On several dynamical properties of shifts acting on directed trees Abakumov, Evgeny Abbar, Arafat Functional Analysis 47A16, 05C05, 47B37, 46B45 This paper explores the notions of $\mathcal{F}$-transitivity and topological $\mathcal{F}$-recurrence for backward shift operators on weighted $\ell^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal{F}$ represents a Furstenberg family of subsets of $\mathbb{N}_0$. In particular, we establish the equivalence between recurrence and hypercyclicity of these operators on unrooted directed trees. For rooted directed trees, a backward shift operator is hypercyclic if and only if it possesses an orbit of a bounded subset that is weakly dense. |
| title | On several dynamical properties of shifts acting on directed trees |
| topic | Functional Analysis 47A16, 05C05, 47B37, 46B45 |
| url | https://arxiv.org/abs/2402.05038 |