Complex caustics of the elliptic billiard - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Arnold Mathematical Journal Année : 2020

Complex caustics of the elliptic billiard

Résumé

The article studies a generalization of the elliptic billiard to the complex domain. We show that the billiard orbits also have caustics, and that the number of such caustics is bigger than for the real case. For example, for a given ellipse E, there exist exactly two confocal ellipses such that the triangular orbits of E are circumscribed about one of them, and each tangent line to one of those ellipses is a side of a triangular orbit. In the case of 4-periodic orbits, we get generically three caustics. We also give an upper bound on the number of caustics for orbits with a fixed number of sides, and explain how to compute its exact value.
Fichier principal
Vignette du fichier
article.pdf (418.02 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03151416 , version 1 (24-02-2021)

Identifiants

Citer

Corentin Fierobe. Complex caustics of the elliptic billiard. Arnold Mathematical Journal, 2020, ⟨10.1007/s40598-020-00152-w⟩. ⟨hal-03151416⟩
10 Consultations
121 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More