Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-conformal deformations of nonlinearizable germs   Let $f(z) = e^{2\pi i \alpha}z + O(z^2), \alpha \in \mathbb{R}$ be a germ of
holomorphic diffeomorphism in $\mathbb{C}$. For $\alpha$ rational and $f$ of
infinite order, the space of conformal conjugacy classes of germs topologically
conjugate to $f$ is parametrized by the Ecalle-Voronin invariants (and in
particular is infinite-dimensional). When $\alpha$ is irrational and $f$ is
nonlinearizable it is not known whether $f$ admits quasi-conformal
deformations. We show that if $f$ has a sequence of repelling periodic orbits
converging to the fixed point then $f$ embeds into an infinite-dimensional
family of quasi-conformally conjugate germs no two of which are conformally
conjugate.

25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg