TY - BOOK
T1 - Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry
AU - Egea, J.
AU - Ferrer, S.
AU - Meer, van der, J.C.
PY - 2009
Y1 - 2009
N2 - This paper deals with the analysis of Hamiltonian Hopf as well as saddle-centre
bifurcations in 4-DOF systems defined by perturbed isotropic oscillators (1:1:1:1
resonance), in the presence of two quadratic symmetries ¿ and L1. When we nor-
malize the system with respect to the quadratic part of the energy and carry out
a reduction with respect to a 3-torus group we end up with a 1-DOF system with
several parameters on the thrice reduced phase space. Then, we focus our analysis
on the evolution of relative equilibria around singular points of this reduced phase
space. In particular, dealing with the Hamiltonian Hopf bifurcation the `geometric
approach' is used, following the steps set up by one of the authors in the context of
3-DOF systems. In order to see the interplay between integrals and physical param-
eters in the analysis of bifurcations, we consider as perturbation a one-parameter
family, which in particular includes one of the classical Stark-Zeeman models (par-
allel case) in 3 dimensions
AB - This paper deals with the analysis of Hamiltonian Hopf as well as saddle-centre
bifurcations in 4-DOF systems defined by perturbed isotropic oscillators (1:1:1:1
resonance), in the presence of two quadratic symmetries ¿ and L1. When we nor-
malize the system with respect to the quadratic part of the energy and carry out
a reduction with respect to a 3-torus group we end up with a 1-DOF system with
several parameters on the thrice reduced phase space. Then, we focus our analysis
on the evolution of relative equilibria around singular points of this reduced phase
space. In particular, dealing with the Hamiltonian Hopf bifurcation the `geometric
approach' is used, following the steps set up by one of the authors in the context of
3-DOF systems. In order to see the interplay between integrals and physical param-
eters in the analysis of bifurcations, we consider as perturbation a one-parameter
family, which in particular includes one of the classical Stark-Zeeman models (par-
allel case) in 3 dimensions
M3 - Report
T3 - CASA-report
BT - Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry
PB - Technische Universiteit Eindhoven
CY - Eindhoven
ER -