A note on the set of periods for continuous maps of the circle which have degree one

Alsedà, Lluís; Llibre, Jaume

doi:10.1090/S0002-9939-1985-0766543-8

A note on the set of periods for continuous maps of the circle which have degree one
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by Lluís Alsedà and Jaume Llibre

Proc. Amer. Math. Soc. 93 (1985), 133-138

DOI: https://doi.org/10.1090/S0002-9939-1985-0766543-8

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Abstract:

The main result of this paper is to complete Misiurewicz’s characterization of the set of periods of a continuous map $f$ of the circle with degree one (which depends on the rotation interval of $f$). As a corollary we obtain a kind of perturbation theorem for maps of the circle of degree one, and a new algorithm to compute the set of periods when the rotation interval is known. Also, for maps of degree one which have a fixed point, we describe the relationship between the characterizations of the set of periods of Misiurewicz and Block.

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