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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Topological entropy for finite invariant subsets of $ Y$

Authors: Shi Hai Li and Xiang Dong Ye
Journal: Trans. Amer. Math. Soc. 347 (1995), 4651-4661
MSC: Primary 58F03; Secondary 58F08
MathSciNet review: 1321582
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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}{\vert _P} = f{\vert _P}$ which achieves the infimum topological entropies of continuous maps from $ Y$ to itself which agree with $ f$ on $ P$.

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Keywords: Minimum topological entropy, triod, tree
Article copyright: © Copyright 1995 American Mathematical Society

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