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Dynamics in One Complex Variable

 By Xavier Buff (University of Toulouse)

and

John H. Hubbard

(Cornell University and the University of Provence)

 Publication date not yet set

Congratulations  to Xavier Buff, who was awarded, with his colleague Arnoud Cheritat, the 2006 Prix le Conte by the Académie des Sciences of the Institut de France.

The field of dynamics in one complex variable has received a lot of attention over the last 25 years. The object of this book is to make the results of this research accessible to a broader audience. Many of these topics are already covered in existing books, but many others are presented here for the first time in book form. Among these are the Ecalle-Voronin classification of parabolic points, the Yoccoz linearization theorem and the sharpness of the result, puzzle techniques, and Thurston's applications of Teichmuller theory.

Contents

Chapter 1 Introduction to Holomorphic Dynamics

1.1 The dynamical features of a rational map.

1.2 Description of the Julia set

1.3 Description of the Fatou set

1.4 Parameter spaces

 Chapter 2 (Super) Attracting and Repelling Fixed Points

2.1 The attracting and repelling cases

2.2 The superattracting case

2.3 Connectivity of the Mandelbrot set

2.4 Landing property of periodic rays ­ the PLY inequality.

Chapter 3 Parabolic Fixed Points

3.1 The formal classification

3.2 The topological classification

3.3 Fatou coordinates

3.4 The classification theorem

3.5 Inequalities for the formal invariant