Cover Image
Read Now

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

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...

Full description

Bibliographic Details
Main Author: Keller, Karsten
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2000, 2000
Edition:1st ed. 2000
Series:Lecture Notes in Mathematics
Subjects:
Topology
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
LEADER 02177nmm a2200289 u 4500
001 EB000656614
003 EBX01000000000000000509696
005 00000000000000.0
007 cr|||||||||||||||||||||
008 140122 ||| eng
020 |a 9783540455899 
100 1 |a Keller, Karsten 
245 0 0 |a Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set  |h Elektronische Ressource  |c by Karsten Keller 
250 |a 1st ed. 2000 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2000, 2000 
300 |a XII, 208 p  |b online resource 
505 0 |a 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 
653 |a Topology 
653 |a Differential Equations 
653 |a Differential equations 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Lecture Notes in Mathematics 
028 5 0 |a 10.1007/BFb0103999 
856 4 0 |u https://doi.org/10.1007/BFb0103999?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 515.35 
520 |a 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 

Similar Items