Topological polynomials with a simple core

Details Topological polynomials with a simple core Topological polynomials with a simple core

2011-06-24

arxiv.org/abs/1106.5022v1

Mathematics

Dynamical Systems

47 pages, 8 figures

Scientific paper

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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