Complex Dynamics: Twenty-Five Years after the Appearance of the Mandelbrot Set

Preface vii

Indecomposable continua and the Julia sets of rational maps

Douglas K. Childers, John C. Mayer, H. Murat Tuncali,

and E. D. Tymchatyn 1

The H´enon family: The complex horseshoe locus and real parameter space

Eric Bedford and John Smillie 21

Baby Mandelbrot sets adorned with halos in families of rational maps

Robert L. Devaney 37

Blowup points and baby Mandelbrot sets for singularly perturbed rational

maps

Robert L. Devaney, Matt Holzer, and David Uminsky 51

Some remarks on the connectivity of Julia sets for 2-dimensional

diffeomorphisms

Romain Dujardin 63

Rigorous numerical studies of the dynamics of polynomial skew products

of C2

Suzanne Lynch Hruska 85

Accumulation points of iterated function systems

Linda Keen and Nikola Lakic 101

Parabolic perturbation of the family λ tan z

Linda Keen and Shenglan Yuan 115

Polynomial vector fields, dessins d’enfants, and circle packings

Kevin M. Pilgrim 129

Siegel disks whose boundaries have only two complementary domains

James T. Rogers, Jr. 139

Non-uniform porosity for a subset of some Julia sets

Kimberly A. Roth 153

The existence of conformal measures for some transcendental meromorphic

functions

Bartlomiej Skorulski 169

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vi CONTENTS

Open problems

Linda Keen 203