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Transactions of the American Mathematical Society

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Topological entropy for noncompact sets


Author: Rufus Bowen
Journal: Trans. Amer. Math. Soc. 184 (1973), 125-136
MSC: Primary 28A65; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1973-0338317-X
MathSciNet review: 0338317
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Abstract: For $ f:X \to X$ continuous and $ Y \subset X$ a topological entropy $ h(f,Y)$ is defined. For X compact one obtains results generalizing known theorems about entropy for compact Y and about Hausdorff dimension for certain $ Y \subset X = {S^1}$ . A notion of entropy-conjugacy is proposed for homeomorphisms.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0338317-X
Keywords: Entropy, Hausdorff dimension, invariant measure, generic points
Article copyright: © Copyright 1973 American Mathematical Society

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