Real Analysis Exchange

Topological entropy and the preimage structure of maps.

Zbigniew H. Nitecki

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Abstract

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 results are stated with at most a sketch of the proof. The informed reader will recognize imagery from Bowen's exposition of topological entropy [Bow78] which I have freely adopted for motivation.

Article information

Source
Real Anal. Exchange, Volume 29, Number 1 (2003), 9-42.

Dates
First available in Project Euclid: 9 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860180

Mathematical Reviews number (MathSciNet)
MR2061291

Zentralblatt MATH identifier
1083.37014

Subjects
Primary: 37A02 37B40: Topological entropy

Keywords
entropy topological entropy preimage entropy topological pressure subshift

Citation

Nitecki, Zbigniew H. Topological entropy and the preimage structure of maps. Real Anal. Exchange 29 (2003), no. 1, 9--42. https://projecteuclid.org/euclid.rae/1149860180


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