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On the Structure of Abstract Hubbard Trees and the Space of Abstract Kneading Sequences of Degree Two

Alexandra Kaffl
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Abstract

One of the fundamental properties of the Mandelbrot set is that the set of postcritically finite parameters is structured like a tree. We extend this result to the set of quadratic kneading sequences and show that this space contains no irrational decorations. Along the way, we prove a combinatorial analogue to the correspondence principle of dynamic and parameter rays. Our key tool is to work simultaneously with the two equivalent combinatorial concepts of Hubbard trees and kneading sequences.

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Alexandra Kaffl. 2007-01-05. On the Structure of Abstract Hubbard Trees and the Space of Abstract Kneading Sequences of Degree Two. https://arxiv.org/abs/math/0701182

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