Document Type
Article
Department/Program
Physics
Journal Title
Physical Review E
Pub Date
8-1996
Publisher
American Physical Society
Volume
54
Issue
2
First Page
2033
Abstract
We develop an analytic technique to study the dynamics in the neighborhood of a periodic trajectory of a Hamiltonian system. The theory begins with Poincaré and Birkhoff; major modern contributions are due to Meyer, Arnol'd, and Deprit. The realization of the method relies on local Fourier-Taylor series expansions with numerically obtained coefficients. The procedure and machinery are presented in detail on the example of the ‘‘perpendicular’’ (z=0) periodic trajectory of the diamagnetic Kepler problem. This simple one-parameter problem well exhibits the power of our technique. Thus, we obtain a precise analytic description of bifurcations observed by J.-M. Mao and J. B. Delos [Phys. Rev. A 45, 1746 (1992)] and explain the underlying dynamics and symmetries. © 1996 The American Physical Society.
Recommended Citation
Sadovskii, D. A. and Delos, John B., Bifurcation of the Periodic Orbits of Hamiltonian Systems: An Analysis using Normal Form Theory (1996). Physical Review E, 54(2), 2033-2070.
https://doi.org/10.1103/PhysRevE.54.2033
DOI
https://doi.org/10.1103/PhysRevE.54.2033
