Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-landing hairs in Sierpinski curve Julia sets of transcendental
  entire maps   We consider the family of transcendental entire maps given by
$f_a(z)=a(z-(1-a))\exp(z+a)$ where $a$ is a complex parameter. Every map has a
superattracting fixed point at $z=-a$ and an asymptotic value at $z=0$. For
$a>1$ the Julia set of $f_a$ is known to be homeomorphic to the Sierpi\'nski
universal curve, thus containing embedded copies of any one-dimensional plane
continuum. In this paper we study subcontinua of the Julia set that can be
defined in a combinatorial manner. In particular, we show the existence of
non-landing hairs with prescribed combinatorics embedded in the Julia set for
all parameters $a\geq 3$. We also study the relation between non-landing hairs
and the immediate basin of attraction of $z=-a$. Even as each non-landing hair
accumulates onto the boundary of the immediate basin at a single point, its
closure, nonetheless, becomes an indecomposable subcontinuum of the Julia set.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas