Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal analysis for sets of non-differentiability of Minkowski's
  question mark function   In this paper we study various fractal geometric aspects of the Minkowski
question mark function $Q.$ We show that the unit interval can be written as
the union of the three sets $\Lambda_{0}:=\{x:Q'(x)=0\}$,
$\Lambda_{\infty}:=\{x:Q'(x)=\infty\}$, and $\Lambda_{\sim}:=\{x:Q'(x)$ does
not exist and $Q'(x)\not=\infty\}.$ The main result is that the Hausdorff
dimensions of these sets are related in the following way.
$\dim_{H}(\nu_{F})<\dim_{H}(\Lambda_{\sim})= \dim_{H} (\Lambda_{\infty}) =
\dim_{H} (\mathcal{L}(h_{\mathrm{top}}))<\dim_{H}(\Lambda_{0})=1.$
  Here, $\mathcal{L}(h_{\mathrm{top}})$ refers to the level set of the
  Stern-Brocot multifractal decomposition at the topological entropy
  $h_{\mathrm{top}}=\log2$ of the Farey map $F,$ and $\dim_{H}(\nu_{F})$
denotes the Hausdorff dimension of the measure of maximal entropy of the
dynamical system associated with $F.$ The proofs rely partially on the
multifractal formalism for Stern-Brocot intervals and give non-trivial
applications of this formalism.

26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph