2021/08/25 by Irene De Blasi, Susanna Terracini, De Blasi, Irene +1 · 1 citation
Mathematics · Physics and Astronomy · #37N05 #70F10 #70F16 #70G75 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2108.11159
openalex publication_date 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this work is to continue the analysis, started in arXiv:2105.02108, of the dynamics of a point-mass particle P moving in a galaxy with an harmonic biaxial core, in whose center sits a Keplerian attractive center (e.g. a Black Hole). Accordingly, the plane \mathbb R2 is divided into two complementary domains, depending on whether the gravitational effects of the galaxy's mass distribution or of the Black Hole prevail. Thus, solutions alternate arcs of Keplerian hyperbolae with harmonic ellipses; at the interface, the trajectory is refracted according to Snell's law. The model was introduced in arXiv:1501.05577, in view of applications to astrodynamics. In this paper we address the general issue of periodic and quasi-periodic orbits and associated caustics when the domain is a perturbation of the circle, taking advantage of KAM and Aubry-Mather theories.