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Multiplicity of topological systems
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 10 / October 2024
- Published online by Cambridge University Press:
- 05 February 2024, pp. 2832-2858
- Print publication:
- October 2024
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- Article
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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.
