A note on chaotic billiards with potentials

Vivina L. Barutello, Irene De Blasi

Published 2023-12-03Version 1

In arXiv:2212.01150, the authors provide a sufficient purely geometrical condition on a planar billiard containing a Keplerian center that ensures the chaoticity of the model. This note is intended as a continuation of the analysis in arXiv:2212.01150 in the sense that it provides an investigation of the actual holding of such a condition, starting from the case of an elliptic billiard. Our main result states that an elliptic (but not circular) domain with a Keplerian mass situated almost everywhere in its interior presents a chaotic dynamics both in reflective and refractive models.