The Mandelbrot set, theme and variations / edited by Tan Lei.

Format:

Book

Contributor:

Tan, Lei, 1963- editor.

Series:

London Mathematical Society lecture note series ; 274.

London Mathematical Society lecture note series ; 274

Language:

English

Subjects (All):

Mandelbrot sets.

Physical Description:

1 online resource (xx, 365 pages) : digital, PDF file(s).

Other Title:

The Mandelbrot Set, Theme & Variations

Place of Publication:

Cambridge : Cambridge University Press, 2000.

Language Note:

English

Summary:

The Mandelbrot set is a fractal shape that classifies the dynamics of quadratic polynomials. It has a remarkably rich geometric and combinatorial structure. This volume provides 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. In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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 researchers in dynamical systems and Kleinian groups.

Contents:

Mandelbrot set is universal / C. McMullen

Baby Mandelbrot sets are born in cauliflowers / A. Douady, with the participation of X. Buff, R. Devaney and P. Sentenac

Modulation dans l'ensemble de Mandelbrot / P. Haïssinsky

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

Herman-Światek Theorems with applications / C. Petersen

Perturbation d'une fonction linéarisable ; Indice holomorphe et multiplicateur / H. Jellouli

Alternative proof of Mañés 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 théorèm d'intégrabilité des structures presque complexes / A. Douady, d'après des notes de X. Buff

Bifurcation of parabolic fixed points / M. Shishikura.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88562-6

1-107-36798-0

1-107-37251-8

1-107-36307-1

1-107-36971-1

1-299-40557-6

1-107-36552-X

0-511-56915-7