Multiplicity of topological systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910704719626240 |
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| author | Burguet, David Shi, Ruxi |
| author_facet | Burguet, David Shi, Ruxi |
| contents | We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a dense linear vector space in the space of real continuous functions on $X$ endowed with the supremum norm. We study some properties of topological systems with finite multiplicity. After giving some examples, we investigate the multiplicity of subshifts with linear growth complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08906 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiplicity of topological systems Burguet, David Shi, Ruxi Dynamical Systems We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a dense linear vector space in the space of real continuous functions on $X$ endowed with the supremum norm. We study some properties of topological systems with finite multiplicity. After giving some examples, we investigate the multiplicity of subshifts with linear growth complexity. |
| title | Multiplicity of topological systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2307.08906 |