**Contemporary Mathematics**

Volume: 396;
2006;
206 pp;
Softcover

MSC: Primary 37;
Secondary 30; 54

Print ISBN: 978-0-8218-3625-5

Product Code: CONM/396

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-0-8218-7986-3
Product Code: CONM/396.E**

List Price: $65.00

Individual Member Price: $52.00

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

Share this page *Edited by *
*Robert L. Devaney; Linda Keen*

Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Fatou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

#### Table of Contents

# Table of Contents

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

- Contents v6 free
- Preface vii8 free
- Indecomposable continua and the Julia sets of rational maps 110 free
- The Hénan family: The complex horseshoe locus and real parameter space 2130
- Baby Mandelbrot sets adorned with halos in families of rational maps 3746
- Blowup points and baby Mandelbrot sets for singularly perturbed rational maps 5160
- Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms 6372
- Rigorous numerical studies of the dynamics of polynomial skew products of C2 8594
- Accumulation points of iterated function systems 101110
- Parabolic perturbation of the family λ tan z 115124
- Polynomial vector fields, dessins d'enfants, and circle packings 129138
- Siegel disks whose boundaries have only two complementary domains 139148
- Non-uniform porosity for a subset of some Julia sets 153162
- The existence of conformal measures for some transcendental meromorphic functions 169178
- Open problems 203212

#### Readership

Graduate students and research mathematicians interested in complex analysis and dynamical systems.