Multiplicity of topological systems

David Burguet; Ruxi Shi

doi:10.1017/etds.2023.118

Multiplicity of topological systems

David Burguet
, Ruxi Shi

École Polytechnique

Sorbonne Université

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We define the topological multiplicity of an invertible topological system (X, T) as the minimal number k of real continuous functions f₁, . . . , f_k such that the functions f_i ◦ Tⁿ, n ∈ Z, 1 ≤ i ≤ 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.

langue originale	Anglais
Pages (de - à)	2832-2858
Nombre de pages	27
journal	Ergodic Theory and Dynamical Systems
Volume	44
Numéro de publication	10
Les DOIs	https://doi.org/10.1017/etds.2023.118
état	Publié - 1 oct. 2024

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10.1017/etds.2023.118

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title = "Multiplicity of topological systems",

abstract = "We define the topological multiplicity of an invertible topological system (X, T) as the minimal number k of real continuous functions f1, . . . , fk such that the functions fi ◦ Tn, n ∈ Z, 1 ≤ i ≤ 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.",

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AB - We define the topological multiplicity of an invertible topological system (X, T) as the minimal number k of real continuous functions f1, . . . , fk such that the functions fi ◦ Tn, n ∈ Z, 1 ≤ i ≤ 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.

KW - entropy

KW - ergodic theory

KW - topological dynamics

KW - topological multiplicity

KW - topological rank

U2 - 10.1017/etds.2023.118

DO - 10.1017/etds.2023.118

M3 - Article

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SP - 2832

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JO - Ergodic Theory and Dynamical Systems

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ER -

Multiplicity of topological systems

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