Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of infinitely generated nicely expanding rational semigroups
  and the inducing method   We investigate the dynamics of semigroups of rational maps on the Riemann
sphere. To establish a fractal theory of the Julia sets of infinitely generated
semigroups of rational maps, we introduce a new class of semigroups which we
call nicely expanding rational semigroups. More precisely, we prove Bowen's
formula for the Hausdorff dimension of the pre-Julia sets, which we also
introduce in this paper. We apply our results to the study of the Julia sets of
non-hyperbolic rational semigroups. For these results, we do not assume the
cone condition, which has been assumed in the study of infinite contracting
iterated function systems. Similarly, we show that Bowen's formula holds for
the limit set of a contracting conformal iterated function system without the
cone condition.

3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org