Physics-Mechanics: Nonlinear dynamics and chaos

Combinations of Complex Dynamical Systems

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Title (user) : Combinations of Complex Dynamical SystemsISBN : 3540201734,9783540201731ISSN : 0075-8434DOI : 10.1007/b14147GoogleBook ID : GI6auAEACAAJOpenLibrary ID : OL9054374MEdition : 1Series : Lecture Notes in Mathematics 1827Authors (user) : Kevin...
Description

Title (user) : Combinations of Complex Dynamical Systems

ISBN : 3540201734,9783540201731

ISSN : 0075-8434

DOI : 10.1007/b14147

GoogleBook ID : GI6auAEACAAJ

OpenLibrary ID : OL9054374M

Edition : 1

Series : Lecture Notes in Mathematics 1827

Authors (user) : Kevin M. Pilgrim (auth.)

Authors (google) : Kevin M. Pilgrim

Publisher : Springer-Verlag Berlin Heidelberg

Language : English

Publication Date : 2003

File Format : pdf

Categories : Differentiable dynamical systems


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Description (user) :

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.


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Description (google) :
The author presents the fundamentals of the ergodic theory of point transformations and several advanced topics of intense research. The study of dynamical systems forms a vast and rapidly developing field even when considering only activity whose methods derive mainly from measure theory and functional analysis. Each of the basic aspects of ergodic theory--examples, convergence theorems, recurrence properties, and entropy--receives a basic and a specialized treatment. The author's accessible style and the profusion of exercises, references, summaries, and historical remarks make this a useful book for graduate students or self study.


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Table of contents :
1 Introduction....Pages 1-35
2 Preliminaries....Pages 37-48
3 Combinations....Pages 49-57
4 Uniqueness of combinations....Pages 59-68
5 Decomposition....Pages 69-77
6 Uniqueness of decompositions....Pages 79-81
7 Counting classes of annulus maps....Pages 83-88
8 Applications to mapping class groups....Pages 89-94
9 Examples....Pages 95-103
10 Canonical Decomposition Theorem....Pages 105-109
References....Pages 111-116

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