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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1321582-4
PII: S 0002-9947(1995)1321582-4
Keywords: Minimum topological entropy, triod, tree
Article copyright: © Copyright 1995 American Mathematical Society