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Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory 1st ed. 2010 [Kõva köide]

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  • Formaat: Hardback, 268 pages, kõrgus x laius: 235x165 mm, kaal: 675 g, XII, 268 p., 1 Hardback
  • Sari: Linear Operators and Linear Systems 208
  • Ilmumisaeg: 27-May-2010
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3034605080
  • ISBN-13: 9783034605083
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Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory 1st ed. 2010Suurem pilt
  • Formaat: Hardback, 268 pages, kõrgus x laius: 235x165 mm, kaal: 675 g, XII, 268 p., 1 Hardback
  • Sari: Linear Operators and Linear Systems 208
  • Ilmumisaeg: 27-May-2010
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3034605080
  • ISBN-13: 9783034605083
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783034605083.html
Märksõnad:
Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.



This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröders and Abels functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.

Arvustused

From the reviews:

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. This well-written book is a good-organized research monograph in the field of Complex Dynamical Systems. It can be highly recommended for experts in Functional Analysis and Dynamical Systems.­­­ (Igor Andrianov, Zentralblatt MATH, Vol. 1198, 2010)

This monograph represents a systematic survey of the topic. All the results are accompanied by detailed proofs. The book is definitely useful for specialists in geometric function theory and operator theory. It is accessible and should be of interest to mathematicians and students familiar with the standard university course of complex analysis. (Pavel A. Gumenuk, Mathematical Reviews, Issue 2012 c)

Preface ix
1 Geometric Background
1(16)
1.1 Some classes of univalent functions
1(6)
1.1.1 Starlike functions
1(1)
1.1.2 Class S[ 0]. Nevanlinna's condition
2(1)
1.1.3 Classes S[ τ], τ Э Δ. Hummel's representation
3(1)
1.1.4 Spirallike functions. Spacek's condition
4(2)
1.1.5 Close-to-convex and φ-like functions
6(1)
1.2 Boundary behavior of holomorphic functions
7(3)
1.3 The Julia-Wolff-Caratheodory and Denjoy-Wolff Theorems
10(3)
1.4 Functions of positive real part
13(4)
2 Dynamic Approach
17(22)
2.1 Semigroups and generators
17(2)
2.2 Flow invariance conditions and parametric representations of semigroup generators
19(4)
2.3 The Denjoy-Wolff and Julia-Wolff-Caratheodory Theorems for semigroups
23(2)
2.4 Generators with boundary null points
25(9)
2.5 Univalent functions and semi-complete vector fields
34(5)
3 Starlike Functions with Respect to a Boundary Point
39(24)
3.1 Robertson's classes. Robertson's conjecture
39(2)
3.2 Auxiliary lemmas
41(3)
3.3 A generalization of Robertson's conjecture
44(2)
3.4 Angle distortion theorems
46(10)
3.4.1 Smallest exterior wedge
46(3)
3.4.2 Biggest interior wedge
49(7)
3.5 Functions convex in one direction
56(7)
4 Spirallike Functions with Respect to a Boundary Point
63(32)
4.1 Spirallike domains with respect to a boundary point
63(6)
4.2 A characterization of spirallike functions with respect to a boundary point
69(4)
4.3 Subordination criteria for the class Spiralμ[ 1]
73(2)
4.4 Distortion Theorems
75(15)
4.4.1 `Spiral angle' distortion theorems
75(4)
4.4.2 Growth estimates for semigroup generators
79(2)
4.4.3 Growth estimates for spirallike functions
81(3)
4.4.4 Classes G (μ, β)
84(6)
4.5 Covering theorems for starlike and spirallike functions
90(5)
5 Kœnigs Type Starlike and Spirallike Functions
95(26)
5.1 Schroder's and Abel's equations
95(4)
5.2 Remarks on stochastic branching processes
99(4)
5.3 Kœnigs' linearization model for dilation type semigroups. Embeddings
103(2)
5.4 Valiron's type linearization models for hyperbolic type semigroups. Embeddings
105(7)
5.5 Pommerenke's and Baker-Pommerenke's linearization models for semigroups with a boundary sink point
112(7)
5.5.1 Pommerenke's linearization model for automorphic type mappings
112(4)
5.5.2 Baker-Pommerenke's model for non-automorphic type self-mappings
116(1)
5.5.3 Higher order angular differentiability at boundary fixed points. A unified model
117(2)
5.6 Embedding property via Abel's equation
119(2)
6 Rigidity of Holomorphic Mappings and Commuting Semigroups
121(32)
6.1 The Burns-Krantz theorem
122(6)
6.2 Rigidity of semigroup generators
128(5)
6.3 Commuting semigroups of holomorphic mappings
133(20)
6.3.1 Identity principles for commuting semigroups
133(7)
6.3.2 Dilation type
140(4)
6.3.3 Hyperbolic type
144(2)
6.3.4 Parabolic type
146(7)
7 Asymptotic Behavior of One-parameter Semigroups
153(42)
7.1 Dilation case
154(5)
7.1.1 General remarks and rates of convergence
154(3)
7.1.2 Argument rigidity principle
157(2)
7.2 Hyperbolic case
159(14)
7.2.1 Criteria for the exponential convergence
159(9)
7.2.2 Angular similarity principle
168(5)
7.3 Parabolic case
173(22)
7.3.1 Discrete case
173(3)
7.3.2 Continuous case
176(8)
7.3.3 Universal asymptotes
184(11)
8 Backward Flow Invariant Domains for Semigroups
195(26)
8.1 Existence
195(10)
8.2 Maximal FIDs. Flower structures
205(3)
8.3 Examples
208(3)
8.4 Angualar characteristics of flow invariant domains
211(5)
8.5 Additional remarks
216(5)
9 Appendices
221(26)
9.1 Controlled Approximation Problems
221(19)
9.1.1 Setting of approximation problems
221(2)
9.1.2 Solutions of approximation problems
223(8)
9.1.3 Perturbation formulas
231(9)
9.2 Weighted semigroups of composition operators
240(7)
Bibliography 247(10)
Subject Index 257(4)
Author Index 261(2)
Symbols 263(2)
List of Figures 265