Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frontiers in complex dynamics   Rational maps on the Riemann sphere occupy a distinguished niche in the
general theory of smooth dynamical systems. First, rational maps are
complex-analytic, so a broad spectrum of techniques can contribute to their
study (quasiconformal mappings, potential theory, algebraic geometry, etc.).
The rational maps of a given degree form a finite-dimensional manifold, so
exploration of this {\em parameter space} is especially tractable. Finally,
some of the conjectures once proposed for {\em smooth} dynamical systems (and
now known to be false) seem to have a definite chance of holding in the arena
of rational maps.
  In this article we survey a small constellation of such conjectures centering
around the density of {\em hyperbolic} rational maps --- those which are
dynamically the best behaved. We discuss some of the evidence and logic
underlying these conjectures, and sketch recent progress towards their
resolution.

20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg