Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of postcritically bounded polynomial semigroups II: fiberwise
  dynamics and the Julia sets   We investigate the dynamics of semigroups generated by polynomial maps on the
Riemann sphere such that the postcritical set in the complex plane is bounded.
Moreover, we investigate the associated random dynamics of polynomials.
Furthermore, we investigate the fiberwise dynamics of skew products related to
polynomial semigroups with bounded planar postcritical set. Using uniform
fiberwise quasiconformal surgery on a fiber bundle, we show that if the Julia
set of such a semigroup is disconnected, then there exist families of
uncountably many mutually disjoint quasicircles with uniform dilatation which
are parameterized by the Cantor set, densely inside the Julia set of the
semigroup. Moreover, we give a sufficient condition for a fiberwise Julia set
$J_{\gamma}$ to satisfy that $J_{\gamma}$ is a Jordan curve but not a
quasicircle, the unbounded component of the complement of $J_{\gamma}$ is a
John domain and the bounded component of the complement of $J_{\gamma}$ is not
a John domain. We show that under certain conditions, a random Julia set is
almost surely a Jordan curve, but not a quasicircle. Many new phenomena of
polynomial semigroups and random dynamics of polynomials that do not occur in
the usual dynamics of polynomials are found and systematically investigated.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph