Rotation number of 2-interval piecewise affine maps - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Rotation number of 2-interval piecewise affine maps

José Pedro Gaivao
  • Fonction : Auteur
Michel Laurent
  • Fonction : Auteur
  • PersonId : 974960
Arnaldo Nogueira
  • Fonction : Auteur

Résumé

We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintuple $\p$ of real numbers satisfying inequations. Viewing $f_{\p}$ as a circle map, we show that it has a rotation number $\rho(f_{\p})$ and we compute $\rho(f_{\p})$ as a function of $\p$ in terms of Hecke-Mahler series. As a corollary, we prove that $\rho(f_{\p})$ is a rational number when the components of $\p$ are algebraic numbers.

Dates et versions

hal-03910501 , version 1 (22-12-2022)

Identifiants

Citer

José Pedro Gaivao, Michel Laurent, Arnaldo Nogueira. Rotation number of 2-interval piecewise affine maps. 2022. ⟨hal-03910501⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More