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Degenerate Periodic Orbits and Homoclinic Torus Bifurcation

Bridges, T J and Donaldson, N M (2005) Degenerate Periodic Orbits and Homoclinic Torus Bifurcation Physical Review Letters, 95 (10). ISSN 0031-9007

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Abstract

A one-parameter family of periodic orbits with frequency omega and energy E of an autonomous Hamiltonian system is degenerate when E-'(omega)=0. In this paper, new features of the nonlinear bifurcation near this degeneracy are identified. A new normal form is found where the coefficient of the nonlinear term is determined by the curvature of the energy-frequency map. An important property of the bifurcating "homoclinic torus" is the homoclinic angle and a new asymptotic formula for it is derived. The theory is constructive, and so is useful for physical applications and in numerics.

Item Type: Article
Additional Information: Published in <i>Physical Review Letters,</i> Vol. 95, Iss. 10. Copyright 2005 American Physical Society. Click <a href=http://prl.aps.org/>here</a> to access the journal's website.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:06
Last Modified: 06 Nov 2013 15:19
URI: http://epubs.surrey.ac.uk/id/eprint/128

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