Author： Wagenknecht Thomas
Publisher： Taylor & Francis Ltd
ISSN： 1468-9375
Source： Dynamical Systems: An International Journal, Vol.17, Iss.1, 2002-03, pp. : 29-44
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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 2-medium.
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