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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.

Dynamics -- Statistical methods. --- Linear models (Statistics). --- Statistics. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Differentiable dynamical systems. --- Linear models (Statistics) --- Univalent functions. --- Functional equations. --- Semigroups. --- Equations, Functional --- Functions, Schlicht --- Functions, Simple --- Functions, Univalent --- Schlicht functions --- Simple functions --- Models, Linear (Statistics) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Mathematics. --- Difference equations. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- System theory. --- Dynamical Systems and Ergodic Theory. --- Functions of a Complex Variable. --- Systems Theory, Control. --- Difference and Functional Equations. --- Functional analysis --- Group theory --- Functions of complex variables --- Geometric function theory --- Mathematical models --- Mathematical statistics --- Statistics --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Systems theory. --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy