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- Title
On the structure of abstract Hubbard trees and the space of abstract kneading sequences of degree two.
- Authors
ALEXANDRA KAFFL
- 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.
- Subjects
MANDELBROT sets; DIMENSION theory (Topology); MULTIFRACTALS; FRACTALS; QUANTUM theory
- Publication
Ergodic Theory & Dynamical Systems, 2007, Vol 27, Issue 4, p1215
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/S0143385706000587