Periodic orbits in the logarithmic potential

Details Periodic orbits in the logarithmic potential Periodic orbits in the logarithmic potential

2008-07-17

arxiv.org/abs/0807.2793v1

Astronomy and Astrophysics (2008), vol. 489, pp. 1055--1063

Astronomy and Astrophysics

Astrophysics

10 pages, 9 figures, accepted for publication on Astronomy and Astrophysics

Scientific paper

10.1051/0004-6361:200810023

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms. The solutions of the equations of motion corresponding to periodic orbits are obtained as series expansions computed by inverting the normalizing canonical transformation. To improve the convergence of the series a resummation based on a continued fraction may be performed. This method is analogous to that looking for approximate rational solutions (Prendergast method). It is shown that with a normal form truncated at the lowest order incorporating the relevant resonance it is possible to construct quite accurate solutions both for normal modes and periodic orbits in general position.

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