Relevance of the 1:1 resonance in galactic dynamics

Details Relevance of the 1:1 resonance in galactic dynamics Relevance of the 1:1 resonance in galactic dynamics

2011-10-04

arxiv.org/abs/1110.0630v2

Astronomy and Astrophysics

Astrophysics

Galaxy Astrophysics

Corrected typos, to appear on the European Physical Journal Plus. arXiv admin note: text overlap with arXiv:0906.3138v1

Scientific paper

This paper aims to illustrate the applications of resonant Hamiltonian normal forms to some problems of galactic dynamics. We detail the construction of the 1:1 resonant normal form corresponding to a wide class of potentials with self-similar elliptical equi-potentials and apply it to investigate relevant features of the orbit structure of the system. We show how to compute the bifurcation of the main periodic orbits in the symmetry planes of a triaxial ellipsoid and in the meridional plane of an axi-symmetric spheroid and briefly discuss how to refine these results with higher-order approaches.

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