Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension spectrum of infinite self-affine iterated function systems   Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its
dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be
realised as the dimension of some subsystem of $\mathcal{F}$. In the case where
$\mathcal{F}$ is a conformal IFS, the properties of the dimension spectrum have
been studied by several authors. In this paper we investigate for the first
time the properties of the dimension spectrum when $\mathcal{F}$ is a
non-conformal IFS. In particular, unlike dimension spectra of conformal IFS
which are always compact and perfect (by a result of Chousionis, Leykekhman and
Urba\'{n}ski, Selecta 2019), we construct examples to show that
$D(\mathcal{F})$ need not be compact and may contain isolated points.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org