Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Possible Limit Functions on a Fatou Component in non-Autonomous
  Iteration   The possibilities for limit functions on a Fatou component for the iteration
of a single polynomial or rational function are well understood and quite
restricted. In non-autonomous iteration, where one considers compositions of
arbitrary polynomials with suitably bounded degrees and coefficients, one
should observe a far greater range of behaviour. We show this is indeed the
case and we exhibit a bounded sequence of quadratic polynomials which has a
bounded Fatou component on which one obtains as limit functions every member of
the classical Schlicht family of normalized univalent functions on the unit
disc. The proof is based on quasiconformal surgery and the use of high iterates
of a quadratic polynomial with a Siegel disc which closely approximate the
identity on compact subsets. Careful bookkeeping using the hyperbolic metric is
required to control the errors in approximating the desired limit functions and
ensure that these errors ultimately tend to zero.

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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th