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
EcalleVoronin 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
