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Dynamics in One Complex Variable

Xavier Buff (University of Toulouse)
John H. Hubbard (Cornell University and the University Aix-Marseille)

No publication date has been set.

The field of dynamics in one complex variable has received a lot of attention over the last 30 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.

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

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