Dynamics on the Riemann Sphere: A Bodil Branner Festschrift

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European Mathematical Society, 2006 - Mathematics - 222 pages
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Dynamics on the Riemann Sphere presents a collection of original research articles by leading experts in the area of holomorphic dynamics. These papers arose from the symposium Dynamics in the Complex Plane, held on the occasion of the 60th birthday of Bodil Branner. Topics covered range from Lattès maps to cubic polynomials over rational maps with Sierpinsky Carpets and Gaskets as Julia sets, as well as rational and entire transcendental maps with Herman rings. Contributors include Artur Avila (Paris VI, France), Arnault Chéritat (Toulouse, France), Robert L. Devaney (Boston, USA), Adrien Douady (Orsay, France), Nuria Fagella (Barcelona, Spain), Christian Henriksen (Lyngby, Denmark), Wolf Jung (Aachen, Germany), Tomoki Kawahira (Kyoto, Japan), Tan Lei (Cergy Pontoise, France), Mikhail Lyubich (Stony Brook, USA), Carsten Lunde Petersen (Roskilde, Denmark), John Milnor (Stony Brook, USA), Pascale Roesch (Lille, France).
 

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Contents

Introduction
3
BrannerHubbard motions and attracting dynamics
45
Examples of Feigenbaum Julia sets with small Hausdorff dimension
71
Parabolic explosion and the size of Siegel disks in the quadratic family
89
On capture zones for the family z z2 + hz2
121
Homeomorphisms of the Mandelbrot Set
139
Arnold Disks and the Moduli of Herman Rings of
161
Stretching rays and their accumulations following Pia Willumsen
183
Conjectures about the BrannerHubbard motion of Cantor sets in C
209
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