BIFURCATION OF THE PERIODIC-ORBITS OF HAMILTONIAN-SYSTEMS - AN ANALYSIS USING NORMAL-FORM THEORY

We develop an analytic technique to study the dynamics in the neighbou rhood of a periodic trajectory of a Hamiltonian system. The theory beg ins with Poincare and Birkhoff; major modern contributions are due to Meyer, Arnol'd, and Deprit. The realization of the method relies on lo cal Fourier-Taylor series expansions with numerically obtained coeffic ients. The procedure and machinery are presented in detail on the exam ple of the ''perpendicular'' (z = 0) periodic trajectory of the diamag netic Kepler problem. This simple one-parameter problem well exhibits the power of our technique. Thus, we obtain a precise analytic descrip tion of bifurcations observed by J.-M. Mao and J.B. Delos [Phys. Rev. A 45, 1746 (1992)] and explain the underlying dynamics adn symmetries.