A most interesting treatize of iteration of polynomials.

I've just started reading, no results, but it promises much.

http://www.math.cornell.edu/~hubbard/Ite...ubics1.pdf
http://www.math.cornell.edu/~hubbard/Ite...ubics2.pdf
The iteration of cubic polynomial
by

BODIL BRANNER (The Technical University of Denmark and Cornell University, Ithaca, NY, U.S.A.) and

JOHN H. HUBBARD (Corner University, Ithaca, NY, U.S.A.)

( 1988 )

Part I: The global topology of parameter

Table of contents

Introduction ................................ 143

CHAPTER I. Univalent functions in complex analytic dynamics ...... 147

1. Attraction to infinity ....................... 147

2. Parametrizing the space of polynomials ............. 150

3. Compactness of the connectedness locus ............ 153

4. The mapping q~e is close to the identity ............. 156

5. The high level sets of H are spheres ............... 160

CHAPTER II. Wringing the complex structure ............... 165

6. Beltrami forms invariant under a polynomial .......... 166

7. Analytic dependence on parameters ............... 169

8. Stretching and wringing the complex structure ......... 171

9. Continuity on the structural stability set ............. 177

10. Continuity for cubic polynomials ................. 179

CHAPTER III. The global topology of parameter space .......... 183

11. Fibrations ............................. 184

12. The structure of the fiber, part 1 ................. 185

13. The structure of the fiber, part 2 ................. 193

14. The global topology of parameter space ............. 197

References ................................. 205

Also the webpage of John Hubbard has a lot of material whose titles (and cooperations) look promising...

Gottfried