Result: Multiplicity of topological systems

Title:
Multiplicity of topological systems
Authors:
Burguet, David, Shi, Ruxi
Source:
Ergodic Theory and Dynamical Systems. 44:2832-2858
Publication Status:
Preprint
Publisher Information:
Cambridge University Press (CUP), 2024.
Publication Year:
2024
Subject Terms:
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), topological rank, ergodic theory, topological dynamics, topological multiplicity, FOS: Mathematics, Symbolic dynamics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 0101 mathematics, entropy, 01 natural sciences, Dynamics in general topological spaces
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1469-4417
0143-3857
DOI:
10.1017/etds.2023.118
DOI:
10.48550/arxiv.2307.08906
Access URL:
http://arxiv.org/abs/2307.08906
Rights:
Cambridge Core User Agreement
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....67a213e5e59f6e585e460299927562fd
Database:
OpenAIRE

Further Information

We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number k of real continuous functions $f_1,\ldots , f_k$ 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.