Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory

ISBN-13: 9783034605083 / Angielski / Twarda / 2010 / 268 str.

Mark Elin; David Shoikhet

Opis

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, Schroder 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."

Recenzje

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)

Spis treści

Geometric Background.- Dynamic Approach.- Starlike Functions with Respect to a Boundary Point.- Spirallike Functions with Respect to a Boundary Point.- Kœnigs Type Starlike and Spirallike Functions.- Rigidity of Holomorphic Mappings and Commuting Semigroups.- Asymptotic Behavior of One-parameter Semigroups.- Backward Flow Invariant Domains for Semigroups.- Appendices.

Blurb

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.