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Linearization Models for Complex Dynamical Systems [electronic resource] :Topics in Univalent Functions, Functional Equations and Semigroup Theory Mark Elin / by David Shoikhet, Mark Elin.

by Shoikhet, David [author.]; Elin, Mark [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Operator Theory: Advances and Applications: 208Publisher: Basel : Birkhäuser Basel, 2010.Description: XII, 268 p. online resource.ISBN: 9783034605090.Subject(s): Mathematics | Functional equations | Differentiable dynamical systems | Functions of complex variables | Systems theory | Mathematics | Dynamical Systems and Ergodic Theory | Functions of a Complex Variable | Systems Theory, Control | Difference and Functional EquationsDDC classification: 515.39 | 515.48 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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