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.

Philip J. Rippon (Edited by), Gwyneth M. Stallard (Edited by)

9780521683722, Cambridge University Press

Paperback, published 26 June 2008

472 pages, 57 b/w illus. 4 exercises
22.8 x 15.2 x 2.5 cm, 0.66 kg

'Baker's work in transcendental meromorphic functions was both pioneering and legendary and his influence in that and related fields has moved friends, colleagues and former students to produce both survey articles and new results, making this both a satisfying and lively tribute.' SciTech Book News

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.

Introduction
1. Iteration of inner functions and boundaries of components of the Fatou set D. Bargmann
2. Conformal automorphisms of finitely connected regions A. F. Beardon and D. Minda
3. Meromorphic functions with two completely invariant domains W. Bergweiler and A. Eremenko
4. A family of matings between transcendental entire functions and a Fuchsian group S. Bullett and M. Freiberger
5. Singular perturbations of z^n R. Devaney, M. Holzer, D. Look, M. Moreno Rocha and D. Uminsky
6. Residual Julia sets of rational and transcendental functions P. Domínguez and N. Fagella
7. Bank-Laine functions via quasiconformal surgery D. Drasin and J. K. Langley
8. Generalisations of uniformly normal families W. K. Hayman and A. Hinkkanen
9. Entire functions with bounded Fatou components A. Hinkkanen
10. On multiply connected wandering domains of entire functions M. Kisaka and M. Shishikura
11. Fractal measures and ergodic theory of transcendental meromorphic functions J. Kotus and M. Urba?ski
12. Combinatorics of bifurcations in exponential parameter space L. Rempe and D. Schleicher
13. Baker domains P. J. Rippon
14. Escaping points of the cosine family G. Rottenfusser and D. Schleicher
15. Dimensions of Julia sets of transcendental meromorphic functions G. M. Stallard
16. Abel's functional equation and its role in the problem of croissance régulière G. Szekeres.

Subject Areas: Differential calculus & equations [PBKJ], Complex analysis, complex variables [PBKD]