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On the structure of abstract Hubbard trees and the space of abstract kneading sequences of degree two

Published online by Cambridge University Press:  11 June 2007

ALEXANDRA KAFFL
ALEXANDRA KAFFL
Affiliation:
Department of Mathematical Sciences, School of Engineering and Science, International University Bremen, D-28759 Bremen, Germany (e-mail: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1215 - 1238
Copyright
2007 Cambridge University Press

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