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<p><p>this Manuscript Provides An Introduction To The Generation Theory Of Nonlinear One-parameter Semigroups On A Domain Of The Complex Plane In The Spirit Of The Wolff-denjoy And Hille-yoshida Theories. Special Attention Is Given To Evolution Equations Reproduced By Holomorphic Vector Fields On The Unit Disk. A Dynamic Approach To The Study Of Geometrical Properties Of Univalent Functions Is Emphasized. <br> The Book Comprises Six Chapters. The Preliminary Chapter And Chapter 1 Give Expositions To The Theory Of Functions In The Complex Plane, And The Iteration Theory Of Holomorphic Mappings According To Wolff And Denjoy, As Well As To Julia And Caratheodory. Chapter 2 Deals With Elementary Hyperbolic Geometry On The Unit Disk, And Fixed Points Of Those Mappings Which Are Nonexpansive With Respect To The Poincar&#233; Metric. Chapters 3 And 4 Study Local And Global Characteristics Of Holomorphic And Hyperbolically Monotone Vector-fields, Which Yield A Global Description Of Asymptotic Behavior Of Generated Flows. Various Boundary And Interior Flow Invariance Conditions For Such Vector-fields And Their Parametric Representations Are Presented. Applications To Univalent Starlike And

Who reads Semigroups in Geometrical Functions Theory?

Author

David Shoiykhet

Publisher

Springer Netherland

Published

2001

Language

EN

ISBN

9789401596329

Category

nonfiction

Subjects

Mathematics, Stem