Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ruelle operator and transcendental entire maps   If $f$ is a transcendental entire function with only algebraic singularities
we calculate the Ruelle operator of $f$. Moreover, we prove both (i) if $f$ has
a summable critical point, then $f$ is not structurally stable under certain
topological conditions and (ii) if all critical points of $f$ belonging to
Julia set are summable, then there exists no invariant lines fields in the
Julia set.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg