We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given a smooth closed planar domain, a central mass generates a Keplerian potential in it, while outside 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 hold generically in C1. The workflow starts with the existence of a symbolic dynamics and ends with the proof of topological chaos, passing through 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 arXiv:2108.11159 [math.DS] and arXiv:2105.02108 [math.DS].

Chaotic dynamics in refraction galactic billiards

Vivina L. Barutello;Irene De Blasi;Susanna Terracini
2023-01-01

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 a smooth closed planar domain, a central mass generates a Keplerian potential in it, while outside 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 hold generically in C1. The workflow starts with the existence of a symbolic dynamics and ends with the proof of topological chaos, passing through 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 arXiv:2108.11159 [math.DS] and arXiv:2105.02108 [math.DS].
2023
36
4209
4246
https://iopscience.iop.org/article/10.1088/1361-6544/acdec2/meta
billiards, refraction, Kepler problem, symbolic dynamics, heteroclinic connections, topological chaos
Vivina L. Barutello; Irene De Blasi; Susanna Terracini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1894197
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