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...
Κύριος συγγραφέας: | |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2000.
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Έκδοση: | 1st ed. 2000. |
Σειρά: | Lecture Notes in Mathematics,
1732 |
Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.