Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set

• Main Author: Keller, Karsten (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1732
• Subjects: Partial differential equations.; Topology.; Partial Differential Equations.

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...

Table of Contents:

• 1. Introduction: Quadratic iteration and Julia equivalences. The Mandelbrot set
• 2. Abstract Julia sets: Symbolic dynamics of the angle-doubling map. Invariant laminations. Julia equivalences
• 3. The Abstract Mandelbrot set: The Abstract Mandelbrot set - an atlas of Abstract Julia sets. The ordered Abstract Mandelbrot set. Renormalization. Correspondence and Translation Principles
• 4. Abstract and concrete theory: Quadratic iteration. Miscellaneous. Appendix: Invariant and completely invariant factors. Simple statements. Shift-invariant factors. Further interesting examples.