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

2007/01/05 by Alexandra Kaffl, Kaffl, Alexandra
Computer Science · Mathematics · Physics and Astronomy · #37E25 #37F10 #37F20 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.math/0701182

openalex publication_date 2007/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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