Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numbers with integer expansion in the numeration system with negative
  base   In this paper, we study representations of real numbers in the positional
numeration system with negative basis, as introduced by Ito and Sadahiro. We
focus on the set $\Z_{-\beta}$ of numbers whose representation uses only
non-negative powers of $-\beta$, the so-called $(-\beta)$-integers. We describe
the distances between consecutive elements of $\Z_{-\beta}$. In case that this
set is non-trivial we associate to $\beta$ an infinite word
$\boldsymbol{v}_{-\beta}$ over an (in general infinite) alphabet. The
self-similarity of $\Z_{-\beta}$, i.e., the property $-\beta \Z_{-\beta}\subset
\Z_{-\beta}$, allows us to find a morphism under which
$\boldsymbol{v}_{-\beta}$ is invariant. On the example of two cubic irrational
bases $\beta$ we demonstrate the difference between Rauzy fractals generated by
$(-\beta)$-integers and by $\beta$-integers.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas