Chaotic dynamics in refraction galactic billiards

Abstract

Abstract We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given an open and bounded domain D ∈ R 2 with smooth boundary, a central mass generates a Keplerian potential in it, while, in R 2 ∖ D ‾ , a harmonic oscillator-type potential acts. At the interface, Snell’s law of refraction holds. The chaoticity result is obtained by imposing progressive assumptions on the domain, arriving to geometric conditions which holds generically in . The workflow starts with the existence of a symbolic dynamics and ends with the proof of topological chaos. Intermediate results will be the analytic non-integrability and the presence of multiple heteroclinic connections between different equilibrium saddle points. This work can be considered as the final step of the investigation carried on in De Blasi and Terracini (2022 Nonlinear Anal. 218 112766; 2023 Discrete Contin. Dyn. Syst. 43 1269–318).