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For f:X → X continuous and Y ⊂ 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 ⊂ X = S¹ . A notion of entropy-conjugacy is proposed for homeomorphisms.
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Rufus Bowen (1973) studied this question.
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