Matings with laminations
Dynamical Systems
2011-12-21 v1
Abstract
We give a topological description of the space of quadratic rational maps with superattractive two-cycles: its "non-escape locus" M2 (the analog of the Mandelbrot set M) is locally connected, it is the continuous image of M under a canonical map, and it can be described as M (minus the 1/2-limb), mated with the lamination of the basilica. The latter statement is a refined version of a conjecture of Ben Wittner, which in its original version requires local connectivity of M to even be stated. Our methods of mating with a lamination also apply to dynamical matings of certain non-locally connected Julia sets.
Keywords
Cite
@article{arxiv.1112.4780,
title = {Matings with laminations},
author = {Dzmitry Dudko},
journal= {arXiv preprint arXiv:1112.4780},
year = {2011}
}