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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).


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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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bridges, T
Donaldson, N M
Date : 1 January 2005
DOI : 10.1103/PhysRevLett.95.104301
Additional Information : Published in <i>Physical Review Letters,</i> Vol. 95, Iss. 10. Copyright 2005 American Physical Society. Click <a href=>here</a> to access the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:06
Last Modified : 16 Jan 2019 16:18

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