Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Une propri\'et\'e de transfert en approximation diophantienne   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 $x \longmapsto x+\omega$ 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 precisely, 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.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics