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Complete orbits for twist maps on the plane: the case of small twist

Published online by Cambridge University Press:  17 November 2010

MARKUS KUNZE  and
RAFAEL ORTEGA
MARKUS KUNZE
Affiliation:
Universität Duisburg-Essen, Fakultät für 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

In this article we consider twist maps that are non-periodic (and hence are defined on the plane rather than on the cylinder) and have small twist at infinity. Under natural assumptions the existence of infinitely many bounded orbits is established, and furthermore it is proved that unbounded orbits follow bounded orbits for long times. An application is given to the Fermi–Ulam ping-pong model with a non-periodic moving wall.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 5 , October 2011 , pp. 1471 - 1498
Copyright
Copyright © Cambridge University Press 2010

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