Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational Parameter Rays of The Multibrot Sets   We prove a structure theorem for the multibrot sets, which are the higher
degree analogues of the Mandelbrot set, and give a complete picture of the
landing behavior of the rational parameter rays and the bifurcation phenomenon.
Our proof is inspired by previous works of Schleicher and Milnor on the
combinatorics of the Mandelbrot set; in particular, we make essential use of
combinatorial tools such as orbit portraits and kneading sequences. However, we
avoid the standard global counting arguments in our proof and replace them by
local analytic arguments to show that the parabolic and the Misiurewicz
parameters are landing points of rational parameter rays.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol