RIGIDITY OF GENERALIZED VEECH 1969/SATAEV 1975 EXTENSIONS OF ROTATIONS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal d'analyse mathématique Année : 2022

RIGIDITY OF GENERALIZED VEECH 1969/SATAEV 1975 EXTENSIONS OF ROTATIONS

Pascal Hubert
  • Fonction : Auteur

Résumé

We look at d-point extensions of a rotation of angle α with r marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of [5]. We study the property of rigidity, in function of the Ostrowski expansions of the marked points by α: we prove that T is rigid when α has unbounded partial quotients, and that T is not rigid when the natural coding of the underlying rotation with marked points is linearly recurrent. But there remains an interesting grey zone between these two cases, in which we have only partial results on the rigidity question; they allow us to build the first examples of non linearly recurrent and non rigid interval exchange transformations. Note that the symbolic dynamical system (X L , S) is minimal (in the usual sense, every orbit is dense) if and only if the language L is minimal as in Definition 1. Definition 3. A language L or the symbolic system (X L , S) is linearly recurrent if there exists K such that in L, every word of length n occurs in every word of length Kn.
Fichier principal
Vignette du fichier
fh3.pdf (275.6 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03446721 , version 1 (24-11-2021)

Identifiants

  • HAL Id : hal-03446721 , version 1

Citer

Sébastien Ferenczi, Pascal Hubert. RIGIDITY OF GENERALIZED VEECH 1969/SATAEV 1975 EXTENSIONS OF ROTATIONS. Journal d'analyse mathématique, 2022. ⟨hal-03446721⟩
25 Consultations
22 Téléchargements

Partager

Gmail Facebook X LinkedIn More