Bifurcations into pathology for Hamiltonian systems
type: Item
instance of: scholarly article
title: Bifurcations into pathology for Hamiltonian systems
zbMATH Open document ID: 0652.34052
DOI: 10.1016/0022-0396(88)90149-0
author: K. Mischaikow
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: A two degrees of freedom potential (Hamiltonian) system is considered where the origin is a non-degenerate local maximum. The total energy level is considered as a bifurcation parameter. In the example treated periodic orbits bifurcate at a certain energy level through simultaneous homoclinic bifurcations. Introducing a second bifurcation parameter a still higher pathology occurs at a critical value.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4063571
zbMATH Keywords: freedom potential
zbMATH Keywords: bifurcation parameter
zbMATH Keywords: simultaneous homoclinic bifurcations
reviewed by: M. Farkas
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90149-0
OpenAlex ID: W1967384084
cites work: Isolated unstable periodic orbits
cites work: Pathology in dynamical systems. I: General theory
cites work: Pathology in dynamical systems. II: Applications
cites work: Pathology in dynamical systems. III: Analytic Hamiltonians
cites work: Q4180600
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Pathology of invariant sets in the monkey saddle
description: scientific article; zbMATH DE number 4063571