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 In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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.

‘… this collection presents important results hitherto unpublished or difficult to find in the literature.’

Source: European Maths Society Journal

'The analytic techniques employed cover an exceptionally broad range and students of mainstream science in search of an appropriate mathematical model to fit their dynamical scheme will find a very solid theoretical base going way beyond the basic concepts.'

Source: Contemporary Physics

… should be studied in depth by any potential worker in this field. This book should remain popular for many years to come.'

Source: The Mathematical Gazette