Transcendental dynamics and complex analysis / edited by Philip J. Rippon, Gwyneth M. Stallard.

Format:

Book

Contributor:

Rippon, P. J., editor.

Stallard, Gwyneth M., editor.

Series:

London Mathematical Society lecture note series ; 348.

London Mathematical Society lecture note series ; 348

Language:

English

Subjects (All):

Functions of complex variables.

Differentiable dynamical systems.

Mathematical analysis.

Physical Description:

1 online resource (xix, 451 pages) : digital, PDF file(s).

Other Title:

Transcendental Dynamics & Complex Analysis

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.

Contents:

Title; Copyright; Contents; Preface; Introduction; 1 Iteration of inner functions and boundaries of components of the Fatou set; 1.INTRODUCTION; 2. ITERATION OF INNER FUNCTIONS; REFERENCES; 2 Conformal automorphisms of finitely connected regions; 1.INTRODUCTION; 2. MÖBIUS MAPS; 3.REDUCTION TO GENERALIZED CIRCULAR REGIONS; 4. CONFORMALLY TRIVIAL GENERALIZED CIRCULAR REGIONS; 5. THE REDUCTION TO CIRCULAR AND PUNCTURED SPHERES; 6. MÖBIUS EQUIVALENCE ANDINVERSIVE DISTANCE; 7. CIRCULATR REGIONS WITH CONNECTIVITY THREE; 8.CIRCULATR REGIONS WITH CONNECTIVITY FOUR; 9. THRICE-PUNCTURED SPHERES

10. THE CROSS-RATIO FUNCTION11. CONFORMAL MöBIUS EQUIVALENCE AND CROSS-RATIOS; 12. FOUR PUNCTURED SPHERES; 13. CONFORMALLY TRIVIAL PUNCTURED SPHERES; 14. MÖBUS EQUIVALENCE AND ABSOLUTE CROSS-RATIOS; 15. THE INTERNAL DIRECT PRODUCT OF AUTOMORPHISMS; 16. A GEOMETRIC VIEW; REFERENCES; 3 Meromorphic functions with two completely invariant domains; 1.INTRODUCTION AND MAIN RESULT; 2. PROOF OF THE THEOREM; 3. EXAMPLES; REFERENCES; 4 A family of matings between transcendental entire functions and a Fuchsian group; 1. THE GROUP T; 2. CORRESPONDENCES AND MATINGS; 3. A FAMILY OF CORRESPONDENCES

4. TRANSCENDENTAL MATINGS5.DYNAMICS OF THE MAP μmR(z); 6.THE FATOU SET OF μmR; 7. CONJUGACIES ON ""TRUNCATED FILLED JULIA SETS""; 8. DYNAMICAL RAYS; 9. REMARKS AND GENERALISATIONS; REFERENCES; 5 Singular perturbations of zn; 1. INTRODUCTION; 2. PRELIMINARIES; 3. THE ESCAPE TRICHOTOMY; 4. THE CASE n = d = 2; 5 .THE CASE n = 1; 6. BURIED SIERPINSKI CURVES; 7. SIERPINSKI GASKET-LIKE JULIA SETS; REFERENCES; 6 Residual Julia sets of rational and transcendental functions; 1. INTRODUCTION; 2. BASIC PROPERTIES OF THE RESIDUAL JULIA SET; 3. THE RESIDUAL JULIA SET FOR RATIONAL FUNCTIONS

4. RESIDUAL JULIA SETS FOR TRANSCENDENTAL ENTIRE FUNCTIONS5. RESIDUAL JULIA SETS FOR TRANSCENDENTAL MEROMORPHIC FUNCTIONS; 6. HAIRS IN THE RESIDUAL JULIA SET; REFERENCES; 7 Bank-Laine functions via quasiconformal surgery; 1. INTRODUCTION; 2. LEMMAS NEEDED FOR THEOREM 1.1; 3. PROOF OF THEOREM 1.1; 4. A RESULT NEEDED FOR THEOREM 1.2; 5. PROOF OF THEOREM 1.2; REFERENCES; 8 Generalisations of uniformly normal families; 1. INTRODUCTION; 2. A SPECIAL CASE; 3. PROOF OF THEOREM 1; 4. APPLICATIONS; REFERENCES; 9 Entire functions with bounded Fatou components; 1. INTRODUCTION; 2. NOTATION

3. HYPERBOLIC GEOMETRY AND SCHOTTKY'S THEOREM4. GROWTH OF ENTIRE FUNCTIONS AND THE COS πρ-THEOREM; 5. BAKER'S ORIGINAL RESULTS; 6. FURTHER RESULTS FOR PERIODIC COMPONENTS OF THE FATOU SET; 7. RESULTS BASED ON GROWTH ALONE; 8. SURVEY OF RESULTS BASED ON THE REGULARITY OF GROWTH; 9. A MINIMUM MODULUS PROBLEM FOR FUNCTIONS OF ORDER < 1=2; 10. PROOFS OF RESULTS BASED ON THE REGULARITY OF GROWTH:SELF-SUSTAINING SPREAD; REFERENCES; 10 On multiply connected wandering domains of entire functions; 1. INTRODUCTION; 2. PROOF OF THEOREM A; 3. SURGERY AND CONFORMAL STRUCTURE

4. CONSTRUCTION (PROOF OF THEOREM B)

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88259-7

1-107-36777-8

1-107-37231-3

1-107-36286-5

0-511-97052-8

1-299-40537-1

1-107-36531-7

0-511-73523-5