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Multiplicity of topological systems

Part of: Ergodic theory

Published online by Cambridge University Press:  05 February 2024

DAVID BURGUET  and
RUXI SHI
DAVID BURGUET*
Affiliation:
Sorbonne Universite, LPSM, 75005 Paris, France (e-mail: ruxi.shi@upmc.fr)
RUXI SHI
Affiliation:
Sorbonne Universite, LPSM, 75005 Paris, France (e-mail: ruxi.shi@upmc.fr)
*
e-mail: david.burguet@upmc.fr
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Abstract

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.

Keywords

topological multiplicitytopological dynamicstopological rankentropyergodic theory

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 27
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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