Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic structures and harmonic measure at bifurcation locus   We study conformal quantities at generic parameters with respect to the
harmonic measure on the boundary of the connectedness loci ${\cal M}_d$ for
unicritical polynomials $f_c(z)=z^d+c$. It is known that these parameters are
structurally unstable and have stochastic dynamics. We prove
$C^{1+\frac{\alpha}{d}-\epsilon}$-conformality, $\alpha = 2-\mbox{HD}\,({\cal
J}_{c_0})$, of the parameter-phase space similarity maps
$\Upsilon_{c_0}(z):\mathbb{C}\mapsto \mathbb{C}$ at typical $c_0\in \partial
{\cal M}_d$ and establish that globally quasiconformal similarity maps
$\Upsilon_{c_0}(z)$, $c_0\in \partial {\cal M}_d$, are $C^1$-conformal along
external rays landing at $c_0$ in $\mathbb{C}\setminus {\cal J}_{c_0}$ mapping
onto the corresponding rays of ${\cal M}_d$. This conformal equivalence leads
to the proof that the $z$-derivative of the similarity map $\Upsilon_{c_0}(z)$
at typical $c_0\in \partial {\cal M}_d$ is equal to $1/{\cal T}'(c_0)$, where
${\cal T}(c_0)=\sum_{n=0}^{\infty}(D(f_{c_0}^n)(c_0))^{-1}$ is the
transversality function.
  The paper builds analytical tools for a further study of the extremal
properties of the harmonic measure on $\partial {\cal M}_d$. In particular, we
will explain how a non-linear dynamics creates abundance of hedgehog
neighborhoods in $\partial {\cal M}_d$ effectively blocking a good access of
$\partial {\cal M}_d $ from the outside.

20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ