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.

### Contents

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. Urbański; 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.

### Review

"... a satisfying and lively tribute... an excellent introduction to Baker and his work"
*Book News*