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.

中文翻译：

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拓扑系统的多重性

我们定义可逆拓扑系统的拓扑多重性 $(X,T)$ 作为最小数k实连续函数 $f_1,\ldots , f_k$ 使得函数 $f_i\circ T^n$ , $n\in {\mathbb {Z}}$ , $1\leq i\leq k,$ 跨越实连续函数空间中的稠密线性向量空间X赋予了最高规范。我们研究具有有限重数的拓扑系统的一些性质。在给出一些例子之后，我们研究了具有线性增长复杂性的子移位的多重性。