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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	2832-2858
Number of pages	27
Journal	Ergodic Theory and Dynamical Systems
Volume	44
Issue number	10
DOIs	https://doi.org/10.1017/etds.2023.118
Publication status	Published - 1 Oct 2024

Keywords

entropy
ergodic theory
topological dynamics
topological multiplicity
topological rank

Access to Document

10.1017/etds.2023.118

Cite this

@article{5bcfa3f01cc848349342ea12c15439b9,

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.",

keywords = "entropy, ergodic theory, topological dynamics, topological multiplicity, topological rank",

author = "David Burguet and Ruxi Shi",

year = "2024",

month = oct,

day = "1",

doi = "10.1017/etds.2023.118",

language = "English",

volume = "44",

pages = "2832--2858",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

number = "10",

}

TY - JOUR

T1 - Multiplicity of topological systems

AU - Burguet, David

AU - Shi, Ruxi

PY - 2024/10/1

Y1 - 2024/10/1

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85184588318

U2 - 10.1017/etds.2023.118

DO - 10.1017/etds.2023.118

M3 - Article

AN - SCOPUS:85184588318

SN - 0143-3857

VL - 44

SP - 2832

EP - 2858

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 10

ER -

Multiplicity of topological systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this