On disjoint dynamical properties and Lipschitz-free spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911887979970560 |
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| author | Cobollo, Ch. Peris, A. |
| author_facet | Cobollo, Ch. Peris, A. |
| contents | The notion of disjoint $\mathcal{A}$-transitivity for a Furstenberg family $\mathcal{A}$ is introduced with the aim to generalize properties derived from disjoint hypercyclic operators. We begin a systematic study by showing some of the basic properties, including necessary conditions to inherit the property on the whole space from an invariant linearly dense set containing the origin. As a consequence, we continue the study of the link between non-linear and linear dynamics through Lipschitz-free spaces by presenting some necessary conditions to obtain disjoint $\mathcal{A}$-transitivity for families of Lipschitz-free operators on $\mathcal{F}(M)$ expressed in terms of conditions in the underlying metric space $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12626 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On disjoint dynamical properties and Lipschitz-free spaces Cobollo, Ch. Peris, A. Functional Analysis Dynamical Systems 47A16, 47B37, 37B02, 46B20, 26A18 The notion of disjoint $\mathcal{A}$-transitivity for a Furstenberg family $\mathcal{A}$ is introduced with the aim to generalize properties derived from disjoint hypercyclic operators. We begin a systematic study by showing some of the basic properties, including necessary conditions to inherit the property on the whole space from an invariant linearly dense set containing the origin. As a consequence, we continue the study of the link between non-linear and linear dynamics through Lipschitz-free spaces by presenting some necessary conditions to obtain disjoint $\mathcal{A}$-transitivity for families of Lipschitz-free operators on $\mathcal{F}(M)$ expressed in terms of conditions in the underlying metric space $M$. |
| title | On disjoint dynamical properties and Lipschitz-free spaces |
| topic | Functional Analysis Dynamical Systems 47A16, 47B37, 37B02, 46B20, 26A18 |
| url | https://arxiv.org/abs/2405.12626 |