Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point

Lluís Alsedá, Jaume Llibre, Michał Misiurewicz, Carles Simó

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

Let f be a continuous map from the circle into itself of degree one, having a periodic orbit of rotation number p/q ≠ 0. If (p, q) = 1 then we prove that f has a twist periodic orbit of period q and rotation number p/q (i.e. a periodic orbit which behaves as a rotation of the circle with angle 2πp/q). Also, for this map we give the best lower bound of the topological entropy as a function of the rotation interval if one of the endpoints of the interval is an integer. © 1985, Cambridge University Press. All rights reserved.
Original languageEnglish
Pages (from-to)501-517
JournalErgodic Theory and Dynamical Systems
Volume5
DOIs
Publication statusPublished - 1 Jan 1985

Fingerprint

Dive into the research topics of 'Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point'. Together they form a unique fingerprint.

Cite this