Closed orbits and their bifurcations in the crossed-fields hydrogen atom

Details Closed orbits and their bifurcations in the crossed-fields hydrogen atom Closed orbits and their bifurcations in the crossed-fields hydrogen atom

2002-12-06

arxiv.org/abs/nlin/0212016v1

Phys. Rev. A 67, 063410 (2003)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevA.67.063410

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension one. Several bifurcation scenarios are described in detail. They are shown to have as their constituents the generic codimension-one bifurcations, which combine into a rich variety of complicated scenarios. We propose heuristic criteria for a classification of closed orbits that can serve to systematize the complex set of orbits.

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