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The number of stable periodic solutions of time-dependent Hamiltonian systems with one degree of freedom

Published online by Cambridge University Press:  01 August 1998

RAFAEL ORTEGA
RAFAEL ORTEGA
Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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Abstract

Let $F:{\Bbb R}^2 \to {\Bbb R}^2$ be a mapping that is analytic and area preserving. If $F\neq \hbox{\it identity}$, then every stable fixed point is isolated.

This result can be applied to prove that the number of stable periodic solutions of a fixed period of certain Hamiltonian systems is finite.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 4 , August 1998 , pp. 1007 - 1018
Copyright
© 1998 Cambridge University Press

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