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Bifurcation of the Periodic Orbits of Hamiltonian Systems: An Analysis using Normal Form Theory
Sadovskii, D. A. Delos, John B.
Sadovskii, D. A.
Delos, John B.
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.
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1996-08-01
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American Physical Society
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Physics
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https://doi.org/10.1103/PhysRevE.54.2033