Intégrabilité 2D et 3D, Structure de phase et Bifurcation des solutions des systèmes Hamiltoniens. Cas des systèmes : Ion piégé, Corps solide de Goryachev-Chaplygin en termes de Sokolov

Abstract

In this paper, the integrable classical case of the Hydrogen atom subjected to three static external fields is investigated. The structuring and evolution of the real phase space are explored. The bifurcation diagram is found and the bifurcations of solutions are discussed. The periodic solutions and their associated periods for singular common-level sets of the first integrals of motion are explicitly described. Numerical investigations are performed for the integrable case by means of Poincaré surfaces of section and comparing them with nearby living nonintegrable solutions, all generic bifurcations that change the structure of the phase space are illustrated; the problem can exhibit regularity-chaos transition over a range of control parameters of system.