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

• Autores: Alexandra Kaffl
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 4, 2007, págs. 1215-1238
• Idioma: inglés
• DOI: 10.1017/s0143385706000587
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• Resumen

  • 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.