Une propriété de transfert en approximation diophantienne
Résumé
Given a vector $\omega \in \mathbb{R}^n$,
the sequence $T_i$ of periods is defined as the sequence of times
of best returns near the origin of the translation
$x\mapsto x+\omega$ on the torus $\mathbb{T}^n$.
In the present paper, we study how the Diophantine
properties of $\omega$ can be expressed considering the
sequence of its periods.
More precidely, we prove that,
if the vector $\omega$ is not resonant,
and if the sequence of periods satisfy the inequality
$T_{i+1} \leq CT_i^{1+\tau}$ with
$\tau<(n-1)^{-1}$, then the
vector $\omega$ is Diophantine.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)