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arXiv · 1106.5022

Topological polynomials with a simple core

Alexander Blokh·Lex Oversteegen·Ross Ptacek·Vladlen Timorin
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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).

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Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin. 2011-06-24. Topological polynomials with a simple core. https://arxiv.org/abs/1106.5022

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