Limit search to available items
Book Cover
E-book

Title Transcendental Dynamics and Complex Analysis / edited by Philip J. Rippon, Gwyneth M. Stallard
Published Cambridge : Cambridge University Press, 2008
Online access available from:
EBSCO eBook Academic Collection    View Resource Record  

Copies

Description 1 online resource (472 pages)
Series London Mathematical Society Lecture Note Series ; no. 348
London Mathematical Society lecture note series ; no. 348
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
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 MATINGS; 5.DYNAMICS OF THE MAP æmR(z); 6.THE FATOU SET OF æmR; 7. CONJUGACIES ON ""TRUNCATED FILLED JULIA SETS""
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
5. THE REDUCTION TO CIRCULAR AND PUNCTURED SPHERES6. MÖBIUS EQUIVALENCE ANDINVERSIVE DISTANCE; 7. CIRCULATR REGIONS WITH CONNECTIVITY THREE; 8.CIRCULATR REGIONS WITH CONNECTIVITY FOUR; 9. THRICE-PUNCTURED SPHERES; 10. THE CROSS-RATIO FUNCTION; 11. 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
8. DYNAMICAL RAYS9. 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
Summary In honour of Noel Baker, a leading exponent of transcendental complex dynamics, this book describes the state of the art in this subject
Notes Title from publishers bibliographic system (viewed 22 Dec 2011)
Subject Differentiable dynamical systems.
Functions of complex variables.
Mathematical analysis.
Form Electronic book
Author Rippon, P. J.
Stallard, Gwyneth M.
ISBN 0511735235 (electronic bk.)
1107362865 (electronic bk.)
9780511735233 (electronic bk.)
9781107362864 (electronic bk.)
(paperback)
(paperback)