Topological entropy for noncompact sets

Abstract

For f : X → X f:X \to X continuous and Y ⊂ X Y \subset X a topological entropy h ( f , Y ) 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 = S 1 Y \subset X = {S^1} . A notion of entropy-conjugacy is proposed for homeomorphisms.