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Complete Orbits for Twist Maps on the Plane: Extensions and Applications

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Abstract

Twist maps (θ 1, r 1) = f (θ, r) on the plane are considered which do not exhibit any kind of periodicity in their dependence on θ. Some general results are obtained which typically yield the existence of infinitely many complete and bounded orbits. Examples that can be treated with this theory include oscillators of the type \({\ddot{x}+V'(x)=p(t)}\) under appropriate hypotheses, the bouncing ball system, and the standard map.

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Authors and Affiliations

  1. Universität Duisburg-Essen, Fachbereich Mathematik, 45117, Essen, Germany

    Markus Kunze

  2. Departamento de Matemática Aplicada, Universidad de Granada, 18071, Granada, Spain

    Rafael Ortega

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  1. Markus Kunze
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  2. Rafael Ortega
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Correspondence to Rafael Ortega.

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Dedicated to Professor R. Johnson on the occasion of his 60th birthday.

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Kunze, M., Ortega, R. Complete Orbits for Twist Maps on the Plane: Extensions and Applications. J Dyn Diff Equat 23, 405–423 (2011). https://doi.org/10.1007/s10884-010-9185-y

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  • DOI: https://doi.org/10.1007/s10884-010-9185-y

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