Deviations for generalized tiling billiards in cyclic polygons - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Deviations for generalized tiling billiards in cyclic polygons

Magali Jay
  • Fonction : Auteur
  • PersonId : 1131305

Résumé

This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asymptotic direction, whereas for N = 3 or 4 almost every trajectory stays at a bounded distance from a line. Moreover, we establish the rate of deviations both in the generic case and in some non generic cases.
Fichier principal
Vignette du fichier
articleV2.pdf (1.21 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04476038 , version 1 (24-02-2024)

Licence

Identifiants

  • HAL Id : hal-04476038 , version 1

Citer

Magali Jay. Deviations for generalized tiling billiards in cyclic polygons. 2024. ⟨hal-04476038⟩
52 Consultations
16 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More