Topological polynomials with a simple core
Dynamical Systems
2016-01-18 v1
Abstract
We define the (dynamical) core of a topological polynomial (and the associated lamination). This notion extends that of the core of a unimodal interval map. Two explicit descriptions of the core are given: one related to periodic objects and one related to critical objects. We describe all laminations associated with quadratic and cubic topological polynomials with a simple core (in the quadratic case, these correspond precisely to points on the Main Cardioid of the Mandelbrot set).
Cite
@article{arxiv.1106.5022,
title = {Topological polynomials with a simple core},
author = {Alexander Blokh and Lex Oversteegen and Ross Ptacek and Vladlen Timorin},
journal= {arXiv preprint arXiv:1106.5022},
year = {2016}
}
Comments
47 pages, 8 figures