Linearization models for complex dynamical systems. Topics in univalent functions, functional equations and semigroup theory.
type: Item
instance of: scholarly article
title: Linearization models for complex dynamical systems. Topics in univalent functions, functional equations and semigroup theory.
zbMATH Open document ID: 1198.37001
DOI: 10.1007/978-3-0346-0509-0
author: Mark Elin
author: David Shoikhet
published in: Operator Theory: Advances and Applications
publication date: 2010-06-22T00:00:00Z
review text: 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. It is assumed that the reader is familiar with Functional Analysis. This book is divided into 9 chapters: Geometric background; Dynamic approach; Starlike functions with respect to a boundary point; Spirallike functions with respect to a boundary point; Koenigs type starlike and spirallike functions; Rigidity of holomorphic mapping and commuting semigroups; Asymptotic behaviour of the one-parameter semigroups; Backward flow invariant domains for semigroups; Appendices. This well-written book is a well-organized research monograph in the field of Complex Dynamical Systems. It can be highly recommended for experts in Functional Analysis and Dynamical Systems.
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 37F45
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 5724516
zbMATH Keywords: complex dynamic system
zbMATH Keywords: linearization
zbMATH Keywords: univalent function
zbMATH Keywords: functional equation
zbMATH Keywords: semigroup
reviewed by: I. V. Andrianov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-0346-0509-0
OpenAlex ID: W2495979436
description: scientific article; zbMATH DE number 5724516