Relevance of the 1:1 resonance in galactic dynamics

TL;DR

This paper explores the application of resonant Hamiltonian normal forms, specifically the 1:1 resonance, to analyze orbit structures and bifurcations in galactic potentials with elliptical symmetry.

Contribution

It develops a method to construct 1:1 resonant normal forms for a broad class of galactic potentials and applies it to study orbit bifurcations in triaxial and axisymmetric systems.

Findings

Identification of bifurcation points for main periodic orbits

Application of normal forms to elliptical galactic potentials

Insights into orbit stability and structure

Abstract

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.