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Linear Operators and Linear Systems

# Linearization Models for Complex Dynamical Systems

## Topics in Univalent Functions, Functional Equations and Semigroup Theory

Authors: Elin, Mark, Shoikhet, David

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• 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
• Includes coverage of relevant prerequisites from iteration theory, fixed point theory and univalent functions
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eBook $109.00 price for USA in USD • ISBN 978-3-0346-0509-0 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Hardcover$149.99
price for USA in USD

This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverage of recent advances in geometric function theory, including the theory of starlike and spirallike functions with respect to a boundary point. Of particular interest is its treatment of continuous time semigroups, about which little has been previously known, emphasizing the use of generation theory for continuous dynamical systems. Such semigroups have important applications in such areas as composition operators, Markov stochastic processes, control theory and optimization. Readers will find in this book a systematic and detailed survey of linearization models for one-parameter continuous semigroups, functional equations, and the different classes of univalent functions which serve as intertwining mappings for these semigroups, along with their applications to various problems of complex dynamics.

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)

• Geometric Background

Pages 1-15

Shoikhet, David (et al.)

• Dynamic Approach

Pages 17-37

Shoikhet, David (et al.)

• Starlike Functions with Respect to a Boundary Point

Pages 39-61

Shoikhet, David (et al.)

• Spirallike Functions with Respect to a Boundary Point

Pages 63-93

Shoikhet, David (et al.)

• Kœnigs Type Starlike and Spirallike Functions

Pages 95-120

Shoikhet, David (et al.)

eBook $109.00 price for USA in USD • ISBN 978-3-0346-0509-0 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Hardcover$149.99
price for USA in USD

## Bibliographic Information

Bibliographic Information
Book Title
Linearization Models for Complex Dynamical Systems
Book Subtitle
Topics in Univalent Functions, Functional Equations and Semigroup Theory
Authors
Series Title
Linear Operators and Linear Systems
Series Volume
208
2010
Publisher
Birkhäuser Basel
Birkhäuser / Springer Basel
eBook ISBN
978-3-0346-0509-0
DOI
10.1007/978-3-0346-0509-0
Hardcover ISBN
978-3-0346-0508-3
Series ISSN
2504-3609
Edition Number
1
Number of Pages
XII, 268
Topics
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