Overview
- Important step towards establishing a bridge between nonlinear semigroup theory, functional and differential equations and geometric function theory
- Self-contained presentation with a complete account of definitions, proofs and references
- Presentation of relevant prerequisites from iteration theory, fixed point theory and univalent functions
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 208)
Part of the book sub series: Linear Operators and Linear Systems (LOLS)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.
This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
Reviews
From the reviews:
“This book is devoted to a systematic and detailed survey and treatment of linearization models for one-parameter continuous semigroups, functional equations, different classes of univalent functions which serve intertwining mappings for these semigroups, and their applications to various problems of complex dynamics. The book is aimed at researches in the field of Nonlinear Dynamics. … This well-written book is a good-organized research monograph in the field of Complex Dynamical Systems. It can be highly recommended for experts in Functional Analysis and Dynamical Systems.” (Igor Andrianov, Zentralblatt MATH, Vol. 1198, 2010)
“This monograph represents a systematic survey of the topic. All the results … are accompanied by detailed proofs. The book is definitely useful for specialists in geometric function theory and operator theory. It is accessible and should be of interest to mathematicians and students familiar with the standard university course of complex analysis.” (Pavel A. Gumenuk, Mathematical Reviews, Issue 2012 c)
Authors and Affiliations
Bibliographic Information
Book Title: Linearization Models for Complex Dynamical Systems
Book Subtitle: Topics in Univalent Functions, Functional Equations and Semigroup Theory
Authors: David Shoikhet, Mark Elin
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-0346-0509-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser / Springer Basel 2010
Hardcover ISBN: 978-3-0346-0508-3Published: 27 May 2010
eBook ISBN: 978-3-0346-0509-0Published: 09 February 2011
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XII, 268
Topics: Dynamical Systems and Ergodic Theory, Functions of a Complex Variable, Systems Theory, Control, Difference and Functional Equations