Bifurcation of quasi-periodic solutions from equilibrium points of reversible dynamical systems
type: Item
instance of: scholarly article
title: Bifurcation of quasi-periodic solutions from equilibrium points of reversible dynamical systems
zbMATH Open document ID: 0644.34043
DOI: 10.1007/BF00251911
author: Jürgen Scheurle
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: The author considers reversible analytic systems in \({\mathbb{R}}^ q\) which depend on a p-dimensional parameter y, \(\dot x=X(y,x)\), where the origin \(x=0\) is an equilibrium point for every value of y. The goal of the paper is to construct quasi-periodic solutions near the origin under some nondegeneracy conditions along the lines of KAM-theory. The main point is that multiple hyperbolic eigenvalues are admitted what was not the case in Moser's original approach. But it must be said that Moser himself formulated the generalized version of his theory in terms of Lie algebras after the Moser-Graff-tori, the first example with multiple hyperbolic eigenvalues, is constructed.
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 4050055
zbMATH Keywords: reversible analytic systems
zbMATH Keywords: KAM-theory
zbMATH Keywords: multiple hyperbolic eigenvalues
reviewed by: Helmut Rüssmann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4050055