Topological Entropy and the Preimage Structure of Maps

  title={Topological Entropy and the Preimage Structure of Maps},
  author={Zbigniew Nitecki},
My aim in this article is to provide an accessible introduction to the notion of topological entropy and (for context) its measure theoretic analogue, and then to present some recent work applying related ideas to the structure of iterated preimages for a continuous (in general non-invertible) map of a compact metric space to itself. These ideas will be illustrated by two classes of examples, from circle maps and symbolic dynamics. My focus is on motivating and explaining definitions; most… CONTINUE READING