Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $k$-transformation on an interval with a hole   Let $T_{k}$ be the expanding map of $[0,1)$ defined by $T_{k}(x) = k x\
\text{mod 1}$, where $k\geq 2$ is an integer. Given $0\leq a<b\leq 1$, let
$\mathcal{W}_{k}(a,b)=\{x\in [0,1)\ \vert \ T_{k}^nx\notin (a,b), \text{ for
all } n\geq 0\}$ be the maximal $T$-invariant subset of $[0,1)\setminus (a,b)$.
We examine the Hausdorff dimension of $\mathcal{W}_{k}(a,b)$ as $a$ and $b$
vary.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th