Complex Dynamics

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

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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 Farou, 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.
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Product details

  • Hardback | 208 pages
  • Providence, United States
  • 8218362509
  • 9788218362509

Table of contents

Indecomposable continua and the Julia sets of rational maps; The Henon family: The complex horseshoe locus and real parameter space; Baby Mandelbrot sets adorned with halos in families of rational maps; Blowup points and baby Mandelbrot sets for singularly perturbed rational maps; Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms; Rigorous numerical studies of the dynamics of polynomial skew products of $mathbb{C}2$; Open problems; Accumulation points of iterated function systems; Parabolic perturbations of the family $lambdatan{z}$; Polynomial vector fields, dessins d'enfants, and circle packings; Siegel disks whose boundaries have only two complementary domains; Non-uniform porosity for a subset of some Julia sets; The existence of conformal measures for some transcendental meromorphic functions
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