Topological entropy of transitive maps of the interval

Abstract

We give a new formula for the topological entropy of a continuous map f of the interval to itself with f² topologically transitive. This leads to stronger forms of well-known results about horseshoes and periodic orbit patterns for continuous maps of the interval in the special case of topologically transitive maps.

Keywords::

• topological entropy
• topological transitivity
• periodic orbit pattern

MSC (2010) Classification::

• 37B40
• 37E05
• 37E15

Acknowledgements

We would like to thank the referees for a careful reading of the paper and several helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^1. Email: [email protected]