Topological entropy for finite invariant subsets of 𝑌

Li, Shi Hai; Ye, Xiang Dong

doi:10.1090/S0002-9947-1995-1321582-4

Topological entropy for finite invariant subsets of $Y$
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by Shi Hai Li and Xiang Dong Ye PDF

Trans. Amer. Math. Soc. 347 (1995), 4651-4661 Request permission

Abstract:

Let $Y$ be the space $\{ z \in {\mathbf {C}}:{z^3} \in [0,1]\}$ with a metric defined by the arc length. Suppose that $f$ is a continuous map from $Y$ to itself and $P$ is a finite $f$-invariant subset. In this paper we construct a continuous map ${C_P}$ from $Y$ to itself satisfying ${C_P}{|_P} = f{|_P}$ which achieves the infimum topological entropies of continuous maps from $Y$ to itself which agree with $f$ on $P$.

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