Presenting papers by researchers in transcendental dynamics and complex analysis, this exciting new and modern book is written in honor of Noel Baker, who laid the foundations of transcendental complex dynamics. 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.
Author(s): Philip J. Rippon, Gwyneth M. Stallard
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 2008
Language: English
Pages: 472
Cover......Page 1
Series Titles......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents ......Page 6
Profile of Noel Baker......Page 7
Preface ......Page 8
Introduction ......Page 10
1 Iteration of inner functions and boundaries of components of the Fatou set ......Page 22
2 Conformal automorphisms of finitely connected regions ......Page 58
3 Meromorphic functions with two completely invariant domains ......Page 95
4 A family of matings between transcendental entire functions and a Fuchsian group ......Page 111
5 Singular perturbations of z^n ......Page 132
6 Residual Julia sets of rational and transcendental functions ......Page 159
7 Bank-Laine functions via quasiconformal surgery ......Page 186
8 Generalisations of uniformly normal families ......Page 200
9 Entire functions with bounded Fatou components ......Page 208
10 On multiply connected wandering domains of entire functions ......Page 238
11 Fractal measures and ergodic theory of transcendental meromorphic functions ......Page 272
12 Combinatorics of bifurcations in exponential parameter space ......Page 338
13 Baker domains ......Page 392
14 Escaping points of the cosine family ......Page 417
15 Dimensions of Julia sets of transcendental meromorphic functions ......Page 446
16 Abel's functional equation and its role in the problem of croissance reguli`ere ......Page 468
