Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Simultaneous Linearization   Given a uniformly quasiregular mapping, there is typically no reason to
assume any relationship between linearizers at different repelling periodic
points. However, in the current paper we prove that in the case where the uqr
map arises as a solution of a Schr\"oder equation then, with some further
natural assumptions, if $L$ is a linearizer at one repelling periodic point,
then $L\circ T$ is a linearizer at another repelling periodic point, where $T$
is a translation. In this sense we say $L$ simultaneously linearizes $f$. In
the plane, an example would be that $e^z$ simultaneously linearizes $z^2$. Our
methods utilize generalized derivatives for quasiregular mappings, including a
chain rule and inverse derivative formula, which may be of independent
interest.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga