Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The infinite derivatives of Okamoto's self-affine functions: an
  application of beta-expansions   Okamoto's one-parameter family of self-affine functions $F_a: [0,1]\to[0,1]$,
where $0<a<1$, includes the continuous nowhere differentiable functions of
Perkins ($a=5/6$) and Bourbaki/Katsuura ($a=2/3$), as well as the Cantor
function ($a=1/2$). The main purpose of this article is to characterize the set
of points at which $F_a$ has an infinite derivative. We compute the Hausdorff
dimension of this set for the case $a\leq 1/2$, and estimate it for $a>1/2$.
For all $a$, we determine the Hausdorff dimension of the sets of points where:
(i) $F_a'=0$; and (ii) $F_a$ has neither a finite nor an infinite derivative.
The upper and lower densities of the digit $1$ in the ternary expansion of
$x\in[0,1]$ play an important role in the analysis, as does the theory of
$\beta$-expansions of real numbers.

23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex