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Complete orbits for twist maps on the plane

Published online by Cambridge University Press:  01 August 2008

MARKUS KUNZE and
RAFAEL ORTEGA
MARKUS KUNZE
Affiliation:
Universität Duisburg-Essen, Fachbereich Mathematik, D-45117 Essen, Germany
RAFAEL ORTEGA
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain (email: rortega@ugr.es)
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Abstract

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Twist maps (θ1,r1)=f(θ,r) are considered in this paper, with no assumption on the periodicity of the map in θ. Under appropriate assumptions, the existence of infinitely many bounded (in r) complete orbits is proven. In particular, our results apply to the class of maps \[ \theta _1=\theta +r,\quad r_1=r+\lambda (\sin \omega _1(\theta +r) +\sin \omega _2(\theta +r)), \] where λ>0 and no arithmetic condition has to be imposed on ω1/ω2.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008, pp. 1197 - 1213
Copyright
Copyright © 2008 Cambridge University Press

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