The Mandelbrot Set, Theme and Variations
Publisher: Cambridge University Press
Published: April 13, 2000
Language: eng
Format: Paperback
Number of pages: 365
ISBN-13: 9780521774765
Subjects: Analytic topology; Probability & statistics; Topology - Fractals; Differential Topology; Mathematics; Science/Mathematics; Topology - General; General; Probability & Statistics - General; Mathematics / Differential Equations; Mathematics-Probability & Statistics - General; Medical-General; Mandelbrot sets
First sentence: We show small Mandelbrot sets are dense in the bifurcation locus for any holomorphic family of rational maps.
Description: 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 In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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.
Notes: London Mathematical Society Lecture Note Series