Slow passage through a saddle-center bifurcation
type: Item
instance of: scholarly article
title: Slow passage through a saddle-center bifurcation
zbMATH Open document ID: 0973.37030
author: Richard Haberman
author: David C. Diminnie
published in: Journal of Nonlinear Science
publication date: 2000-05-07T00:00:00Z
review text: The authors consider slowly varying conservative one-degree of freedom Hamiltonian systems in the case of a saddle-center bifurcation. By using energy-angle coordinates the equation is brought in standard form for the method of averaging. The averaged equation is used to obtain the boundary of the basin of repulsion. Further it is shown that the slow passage of the saddle-center homoclinic orbit consists of a large sequence of nearly saddle-center homoclinic orbits to the strongly nonlinear oscillations before and after the passage.
reviewed by: Jürgen Knobloch
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 1439881
zbMATH Keywords: slowly varying Hamiltonian systems
zbMATH Keywords: saddle-center bifurcation
zbMATH Keywords: slow passage through a separatrix
MaRDI profile type: Publication
full work available at URL: s003329910009
OpenAlex ID: W2051994009
DOI: 10.1007/S003329910009
description: scientific article; zbMATH DE number 1439881