Abstract

A new type of dynamical model, describing the planar motion of a particle in an elliptic galaxy with a central mass, say, a Black Hole, is described. It can be treated as a refraction billiard, where two different forces act in two complementary regions of the space separated by an interface, where a Snell’s law of ray refraction holds. The system is studied by generalising classical results of the Birkhoff billiards, relying on perturbative (KAM theory) and variational (Aubry-Mather theory) approaches. The main focus is on the search for periodic and quasi-periodic orbits for the dynamics, with an eye on its possible chaoticity.

Work in collaboration with Susanna Terracini and Vivina Barutello.

References:

Refraction Periodic Trajectories in Central Mass Galaxies, I. D.B. and S. Terracini, 2021 https://arxiv.org/abs/2105.02108

On some Refraction Billiards, I. D.B. and S. Terracini, 2021 https://arxiv.org/abs/2108.11159