Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
type: Item
instance of: scholarly article
title: Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
zbMATH Open document ID: 0755.35118
DOI: 10.1016/0167-2789(92)90092-2
author: Gregor Kovačič
author: Stephen Wiggins
published in: Physica D
publication date: 1993-01-16T00:00:00Z
review text: In this paper the authors give a new global perturbation technique, fundamentally different from others, for detecting homoclinic and heteroclinic orbits in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two-degree-of- freedom Hamiltonian systems. By this technique, the orbits homoclinic and heteroclinic to fixed points that are created in a resonance resulting from the perturbation are determined, and the conditions under which these homoclinic connections can lead to chaotic dynamics are discussed, and an application to a modified model of the forced and damped sine- Gordon equation developed by Bishop et al. is given.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 91642
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: global permutation techniques
zbMATH Keywords: Hamiltonian systems
MaRDI profile type: Publication
full work available at URL: 0167-2789(92)90092-2
OpenAlex ID: W2038143838
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description: scientific article; zbMATH DE number 91642