IJPAM: Volume 53, No. 4 (2009)
GENERIC ONE-PARAMETER VERSAL UNFOLDINGS OF
SYMMETRIC HAMILTONIAN SYSTEMS IN 1:1 RESONANCE
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: j.c.v.d.meer@tue.nl
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513, MB Eindhoven, 5600, THE NETHERLANDS
e-mail: j.c.v.d.meer@tue.nl
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