Kneading theory and rotation intervals for a class of circle maps of degree one

L. Alseda; F. Manosas

doi:10.1088/0951-7715/3/2/008

Kneading theory and rotation intervals for a class of circle maps of degree one

L. Alseda, F. Manosas

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

The authors give a kneading theory for the class of continuous maps of the circle of degree with a single maximum and a single minimum. For a map of this class they characterise the set of itineraries depending on the rotation interval. From this result they obtain lower and upper bounds of the topological entropy and of the number of periodic orbits of each period. These lower bounds appear to be valid for a general continuous map of the circle of degree one. © 1990 IOP Publishing Ltd.

Original language	English
Pages (from-to)	413-452
Journal	Nonlinearity
Volume	3
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/3/2/008
Publication status	Published - 1 Jan 1990

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abstract = "The authors give a kneading theory for the class of continuous maps of the circle of degree with a single maximum and a single minimum. For a map of this class they characterise the set of itineraries depending on the rotation interval. From this result they obtain lower and upper bounds of the topological entropy and of the number of periodic orbits of each period. These lower bounds appear to be valid for a general continuous map of the circle of degree one. {\textcopyright} 1990 IOP Publishing Ltd.",

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N2 - The authors give a kneading theory for the class of continuous maps of the circle of degree with a single maximum and a single minimum. For a map of this class they characterise the set of itineraries depending on the rotation interval. From this result they obtain lower and upper bounds of the topological entropy and of the number of periodic orbits of each period. These lower bounds appear to be valid for a general continuous map of the circle of degree one. © 1990 IOP Publishing Ltd.

AB - The authors give a kneading theory for the class of continuous maps of the circle of degree with a single maximum and a single minimum. For a map of this class they characterise the set of itineraries depending on the rotation interval. From this result they obtain lower and upper bounds of the topological entropy and of the number of periodic orbits of each period. These lower bounds appear to be valid for a general continuous map of the circle of degree one. © 1990 IOP Publishing Ltd.

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