The quasi-periodic centre-saddle bifurcation
type: Item
instance of: scholarly article
title: The quasi-periodic centre-saddle bifurcation
zbMATH Open document ID: 0936.37028
author: Heinz Hanßmann
published in: Journal of Differential Equations
publication date: 2000-05-22T00:00:00Z
review text: Perturbations of a one-parameter family of Hamiltonian systems, \(H_{\lambda}\), are considered in the paper. It is assumed that for some value of ''bifurcation parameter'' \(\lambda_{0}\) the Hamiltonian system \(H_{\lambda_{0}}\) has lower dimensional normally parabolic invariant tori and quasi-periodic center-saddle bifurcation takes place. In the integrable case such invariant tori bifurcate into normally hyperbolic and elliptic tori. With a KAM-theoretic approach the authors prove that the whole bifurcation scenario with all lower dimensional normally parabolic tori parameterized by pertinent Cantor sets of diophantine frequency vectors persist under small non-integrable perturbations. These result are applied to perturbations of a dynamically symmetric free rigid body, namely, the Euler top.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37N05
Mathematics Subject Classification ID: 37J20
zbMATH DE Number: 1212876
zbMATH Keywords: center-saddle bifurcation
zbMATH Keywords: KAM-theory
zbMATH Keywords: Cantor sets
zbMATH Keywords: rigid body dynamics
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: invariant tori
zbMATH Keywords: hyperbolic tori
zbMATH Keywords: elliptic tori
zbMATH Keywords: diophantine frequency
zbMATH Keywords: Euler top
MaRDI profile type: Publication
full work available at URL: jdeq.1997.3365
OpenAlex ID: W2148714233
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DOI: 10.1006/JDEQ.1997.3365
description: scientific article; zbMATH DE number 1212876