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).
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||1 January 2005|
|Identification Number :||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=http://prl.aps.org/>here</a> to access the journal's website.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:06|
|Last Modified :||06 Nov 2013 15:19|
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