Austrian Early Career Conference 2024

Contribution:
Poster

Authors:
Edward Lilley

Affiliations:
University of Vienna

Title:
Symmetry methods in galactic dynamics

Abstract:
Notions of symmetry and integrability are ubiquitous in physics, and this is especially true when considering the dynamics of self-gravitating systems (e.g. galaxies). A central problem is the calculation of the normal modes of an equilibrium dynamical model. This talk will look at the role played by symmetries in the classification of coordinate systems appropriate for both the dynamical (Hamilton-Jacobi) and gravitational (Poisson) parts of the problem. The focus will be on recent results in the latter case -- in particular, symmetry operators that give rise to appropriate bases of orthogonal functions to represent perturbations of spherically-symmetric, razor-thin disc, or slightly-thickened-disc galaxies (arxiv:2302.06944). Applications of the main mathematical results to other subfields of physics will also be discussed.