Periodic orbits in the logarithmic potential

Abstract

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.

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

References in corpus (6)

• Stellar Dynamics around Black Holes in Galactic Nuclei
• A map for eccentric orbits in triaxial potentials
• On the Orbit Structure of the Logarithmic Potential
• Can galactic nuclei be non-axisymmetric? --- The parameter space of power-law discs
• Stability of axial orbits in galactic potentials
• The pendulum dilemma of fish orbits

Cited by in corpus (6)

• Natural orbit approximations in single power-law potentials
• Transient times, resonances and drifts of attractors in dissipative rotational dynamics
• A Study of the Orbits of the Logarithmic Potential for Galaxies
• Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
• Resonances and bifurcations in axisymmetric scale-free potentials
• The symmetric 1:2 resonance