Heinz HANSSMANN

Institut für Reine und angewandte Mathematik
RWTH Aachen
52056 Aachen
Germany
Heinz@iram.rwth-aachen.de
 

Bifurcations of lower-dimensional tori close to an internal-normal resonance in quasi-periodically forced Hamiltonian systems

Abstract : Let us consider a quasi-periodic time-dependent perturbation of an autonomous Hamiltonian system. Let us focus on an elliptic equilibrium point of the unperturbed Hamiltonian. Under suitable hypotheses, this equilibrium point becomes an invariant torus under the effect of the perturbation, with the same frequencies as the perturbation. The normal frequencies of this torus are a perturbation of the normal frequencies around the initial equilibrium point.

In this work we consider the interaction between these frequencies. We add a parameter to the system such that the internal frequencies are always fixed (hence, the torus is not destroyed because of an internal resonance) and the normal ones move with the parameter. In the talk we will present a numerical study about several bifurcations that take place when the normal and internal frequencies are in resonance. We will also discuss the theoretical support for those bifurcations.