IJPAM: Volume 53, No. 4 (2009)

GENERIC ONE-PARAMETER VERSAL UNFOLDINGS OF
SYMMETRIC HAMILTONIAN SYSTEMS IN 1:1 RESONANCE

J.C. van der Meer
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513, MB Eindhoven, 5600, THE NETHERLANDS
e-mail: [email protected]


Abstract.We consider Hamiltonian systems in 1:1 resonance in the presence of symmetry. We give some new proofs for known results concerning the classification of generic one-parameter deformations of equivariant linear systems and the passing and splitting of eigenvalues. We show that for nonlinear systems in two degrees of freedom the bifurcation of periodic solutions in the generic passing cases can be linearized. We conclude with several examples.

Received: May 14, 2009

AMS Subject Classification: 37J40, 37J15, 37J20

Key Words and Phrases: Hamiltonian system, symmetry, versal unfolding, 1:1 resonance

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 4