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Transcendental Dynamics and Complex Analysis /
In honour of Noel Baker, a leading exponent of transcendental complex dynamics, this book describes the state of the art in this subject.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2008.
|
| Colección: | London Mathematical Society lecture note series ;
no. 348. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 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.
- 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""
- 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.
- 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.