The Mandelbrot set, theme and variations

The Mandelbrot set, theme and variations

by Lei, Tan

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This volume presents a systematic exposition of current knowledge about the Mandelbrot set and presents the latest research in complex dynamics. Topics discussed include the universality and the local connectivity of the Mandelbrot set, parabolic bifurcations, critical circle homeomorphisms, absolutely continuous invariant measures and matings of polynomials, along with the geometry, dimension and local connectivity of Julia sets. Chapters document important results hitherto unpublished or diff…

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Title Statements

  • Full title :The Mandelbrot set, theme and variations / edited by Tan Lei.

Summary

This volume presents a systematic exposition of current knowledge about the Mandelbrot set and presents the latest research in complex dynamics. Topics discussed include the universality and the local connectivity of the Mandelbrot set, parabolic bifurcations, critical circle homeomorphisms, absolutely continuous invariant measures and matings of polynomials, along with the geometry, dimension and local connectivity of Julia sets. Chapters document important results hitherto unpublished or difficult to find in the literature. This book will be of interest to graduate students in mathematics, physics and mathematical biology, as well as to researchers in dynamical systems and Kleinian groups.

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Edition Statements

  • Publication Date:2000.

Publication Statements

Notes

Title from publishers bibliographic system (viewed on 13 Sep 2011).

The Physical Object

  • Description:online resource (xx, 365 s.) : : illustrations

Edition Identifiers

Table of Contents

The Mandelbrot set is universal / C. McMullen -- Baby Mandelbrot sets are born in cauliflowers / A. Douady, with the participation of X. Buff, R. Devaney & P. Sentenac -- Modulation dans l'ensemble de Mandelbrot / P. Haissinsky -- Local connectivity of Julia sets: expository lectures / J. Milnor -- Holomorphic motions and puzzles (following M. Shishikura) / P. Roesch -- Local properties of the Mandelbrot set at parabolic points / Tan L. -- Convergence of rational rays in parameter spaces / C. Petersen and G. Ryd -- Bounded recurrence of critical points and Jakobson's Theorem / S. Luzzatto -- The Herman-Swiatek Theorems with applications / C. Petersen -- Perturbation d'une fonction linearisable / H. Jellouli -- Indice holomorphe et multiplicateur / H. Jellouli -- An alternative proof of Marie's theorem on non-expanding Julia sets / M. Shishikura and Tan L. -- Geometry and dimension of Julia sets / Yin Y.-C. -- On a theorem of M. Rees for the matings of polynomials / M. Shishikura -- Le theoreme d'integrabilite des structures presque complexes / A. Douady, d'apres des notes de X. Buff -- Bifurcation of parabolic fixed points / M. Shishikura.

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Subjects

Mandelbrot set

Writers

Lei, Tan

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