Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of inner functions associated with hyperbolic maps   Let $f$ be a function in the Eremenko-Lyubich class $\mathcal{B}$, and let
$U$ be an unbounded, forward invariant Fatou component of $f$. We relate the
number of singularities of an inner function associated to $f|_U$ with the
number of tracts of $f$. In particular, we show that if $f$ lies in either of
two large classes of functions in $\mathcal{B}$, and also has finitely many
tracts, then the number of singularities of an associated inner function is at
most equal to the number of tracts of $f$.
  Our results imply that for hyperbolic functions of finite order there is an
upper bound -- related to the order -- on the number of singularities of an
associated inner function.

19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph