Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiability and H\"older spectra of a class of self-affine
  functions   This paper studies a large class of continuous functions
$f:[0,1]\to\mathbb{R}^d$ whose range is the attractor of an iterated function
system $\{S_1,\dots,S_{m}\}$ consisting of similitudes. This class includes
such classical examples as P\'olya's space-filling curves, the Riesz-Nagy
singular functions and Okamoto's functions. The differentiability of $f$ is
completely classified in terms of the contraction ratios of the maps
$S_1,\dots,S_{m}$. Generalizing results of Lax (1973) and Okamoto (2006), it is
shown that either (i) $f$ is nowhere differentiable; (ii) $f$ is
non-differentiable almost everywhere but with uncountably many exceptions; or
(iii) $f$ is differentiable almost everywhere but with uncountably many
exceptions. The Hausdorff dimension of the exceptional sets in cases (ii) and
(iii) above is calculated, and more generally, the complete multifractal
spectrum of $f$ is determined.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int