A map for galaxy potentials in resonance cases

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Galaxies, Harmonic Oscillators, Kinematics, Maps, Poincare Problem, Potential Energy, Resonance, Equations Of Motion, Hamiltonian Functions, Numerical Integration, Stability

Scientific paper

We present a general map in order to study the Poincare surface of section for a galactic type potential in the exact resonance case. The potential consists of a two-dimensional harmonic oscillator with a perturbing term of the form x2py2q. The Poincare surface of section generated by the map is compared with that given by the numerical integration of the equations of motions and the agreement is good. The map is also used for study of the stability of the periodic points.

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