Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero

Wagenknecht, Thomas (2002) Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero. Dynamical Systems, 17 (1). pp. 29-44. ISSN 1468-9367

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Abstract

Bifurcations are studied from a fixed point with fourfold eigenvalue zero occurring in a two degrees of freedom Hamiltonian system of second-order ordinary differential equations (ODEs) which is additionally reversible with respect to two different linear involutions. Using techniques from Catastrophe Theory we are led to a codimension 2 problem and obtain two different unfoldings of the singularity related to the hyperbolic and elliptic umbilic, respectively. The analysis of the unfolded systems is essentially concerned with the existence and properties of homoclinic and heteroclinic orbits. The studies are motivated by a problem from nonlinear optics concerning the existence of solitons in a chi^2-medium.

Item Type:	Article
Uncontrolled Keywords:	degenerate equilibrium, unfolding, reversible system, connecting orbits
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
Depositing User:	Thomas Wagenknecht
Date Deposited:	28 Sep 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/616

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