Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonrigidity of piecewise-smooth circle maps   Let $f_{i},$ $i=1,2$ be piecewise-smooth $C^{1}$ circle homeomorphisms with
two break points, $\log Df_{i},$ $i=1,2$ are absolutely continuous on each
continuity intervals of $Df_{i}$ and $D\log Df_{i}\in L^{p}$ for some $p>1.$
Suppose, the jump ratios of $f_{1} $ and $f_{2} $ at their break points do not
coincide but have the same total jumps (i.e. the product of jump ratios) and
identical irrational rotation number of bounded type. Then the conjugation $h$
between $f_{1} $ and $f_{2} $ is a singular function, i.e. it is continuous on
$S^1,$ but $Dh(x)=0$ a.e. with respect to Lebesgue measure.

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex