Unfoldings of quasi-periodic tori in reversible systems
type: Item
instance of: scholarly article
title: Unfoldings of quasi-periodic tori in reversible systems
zbMATH Open document ID: 0820.58050
DOI: 10.1007/BF02218818
author: G. B. Huitema
author: Henk Broer
published in: Journal of Dynamics and Differential Equations
publication date: 1995-04-04T00:00:00Z
review text: It is well known that there exists a great similarity between Hamiltonian and reversible systems. In particular, \textit{J. Moser} [Stable and random motions in dynamical systems. Ann. Math. Stud. 77. Princeton, N. J.: Princeton University Press (1973; Zbl 0271.70009)] showed that the ``classical'' KAM-theorem on the persistence of a (maximal-dimensional) invariant quasi-periodic tori for perturbed Hamiltonian systems also holds in the reversible setting. In the paper a general KAM-theory for reversible systems is given. The cases of both maximal and lower- dimensional quasi-periodic invariant tori are investigated. By virtue of the fact that in some cases additional parameters are needed for the persistence of tori, an unfolding theory for reversible systems is developed.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37C55
zbMATH DE Number: 740269
zbMATH Keywords: unfolding parameters
zbMATH Keywords: reversible systems
zbMATH Keywords: quasi-periodic tori
zbMATH Keywords: KAM-theory
reviewed by: Eugene Ershov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02218818
OpenAlex ID: W1986507099
description: scientific article; zbMATH DE number 740269