Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set
Edition: 1 edition
Publisher: Springer
Published: June 8, 2000
Language: eng
Format: Paperback
Number of pages: 206
ISBN-13: 9783540674344
Subjects: Calculus & mathematical analysis; Topology; Geometry - General; Differentiable Dynamical Systems; Mathematics; Topological Dynamics; Science/Mathematics; Symbolic dynamics; Differential Equations; General; Julia set; Mandelbrot set; Mathematics / Differential Equations; Mathematics-Geometry - General; Medical-General; Quadratic Iteraction; Geometry - Algebraic; Analytic functions; Functions of complex variables
Description: This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.
Notes: Lecture Notes in Mathematics