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.

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.