Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Diophantine approximation related to beta-transformations   For any $\beta>1$, let $T_\beta$ be the classical $\beta$-transformations.
Fix $x_0\in[0,1]$ and a nonnegative real number $\hat{v}$, we compute the
Hausdorff dimension of the set of real numbers $x\in[0,1]$ with the property
that, for every sufficiently large integer $N$, there is an integer $n$ with
$1\leq n\leq N$ such that the distance between $T_\beta^nx$ and $x_0$ is at
most equal to $\beta^{-N\hat{v}}$. This work extends the result of Bugeaud and
Liao \cite{YLiao2016} to every point $x_0$ in unit interval.

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The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin