Linearization models for complex dynamical systems. Topics in univalent functions, functional equations and semigroup theory.
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.
scientific article; zbMATH DE number 5724516