Hamiltonian Normal Forms and Galactic Potentials

TL;DR

This paper reviews how to use detuned resonant normal forms to analyze the dynamics of self-gravitating stellar systems with elliptical equipotentials, revealing stability thresholds and bifurcations.

Contribution

It introduces a method to extract dynamical information from normal forms in galactic potentials, including instability thresholds and bifurcation points.

Findings

Computed instability thresholds of axial orbits.

Identified bifurcation values of low-order boxlets.

Analyzed phase-space fractions around key orbit families.

Abstract

The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several aspects of the dynamics in systems with self-similar elliptical equipotentials. In particular, using energy and ellipticity as parameters, we compute the instability thresholds of axial orbits, bifurcation values of low-order boxlets and phase-space fractions pertaining to the families around them. We also show how to infer something about the singular limit of the potential.