University of Surrey

Test tubes in the lab Research in the ATI Dance Research

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

[img]
Preview
PDF
fulltext.pdf

Download (153kB)

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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmail
Bridges, T Jt.bridges@surrey.ac.uk
Donaldson, N MUNSPECIFIED
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
URI: http://epubs.surrey.ac.uk/id/eprint/128

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800