Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast escaping points of entire functions   Let $f$ be a transcendental entire function and let $A(f)$ denote the set of
points that escape to infinity `as fast as possible' under iteration. By
writing $A(f)$ as a countable union of closed sets, called `levels' of $A(f)$,
we obtain a new understanding of the structure of this set. For example, we
show that if $U$ is a Fatou component in $A(f)$, then $\partial U\subset A(f)$
and this leads to significant new results and considerable improvements to
existing results about $A(f)$. In particular, we study functions for which
$A(f)$, and each of its levels, has the structure of an `infinite spider's
web'. We show that there are many such functions and that they have a number of
strong dynamical properties. This new structure provides an unexpected
connection between a conjecture of Baker concerning the components of the Fatou
set and a conjecture of Eremenko concerning the components of the escaping set.

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The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph