The Mandelbrot set is a fractal shape that classifies the dynamics of quadratic polynomials. It has a remarkably rich geometric and combinatorial structure. This volume provides a systematic exposition of current knowledge about the Mandelbrot set and presents the latest research in complex dynamics. Topics discussed include the universality and the local connectivity of the Mandelbrot set, parabolic bifurcations, critical circle homeomorphisms, absolutely continuous invariant measures and matings of polynomials, along with the geometry, dimension and local connectivity of Julia sets. In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature. This book will be of interest to graduate students in mathematics, physics and mathematical biology, as well as researchers in dynamical systems and Kleinian groups.
Reihe
Sprache
Zielgruppe
Illustrationen
ISBN-13
978-0-511-56915-9 (9780511569159)
Schweitzer Klassifikation
Herausgeber*in
Université de Cergy-Pontoise
Tan Lei has been a professor at the University of Angers since September 2009. Prior to that, he was a teacher and researcher at ENS Lyon, the University of Warwick and the Universite de Cergy-Pontoise.
Introduction L.Tan
Preface J. Hubbard
1. The Mandelbrot set is universal C. McMullen
2. Baby Mandelbrot sets are born in cauliflowers A. Douady, X. Buff, R. Devaney and P. Sentenac
3. Modulation dans l'ensemble de Mandelbrot P. Haïssinsky
4. Local connectivity of Julia sets: expository lectures J. Milnor
5. Holomorphic motions and puzzles (following M. Shishikura) P. Roesch
6. Local properties of the Mandelbrot set at parabolic points L.Tan
7. Convergence of rational rays in parameter spaces C. Petersen and G. Ryd
8. Bounded recurrence of critical points and Jakobson's Theorem S. Luzzatto
9. The Herman-Swiatek theorems with applications C. Petersen
10. Perturbations d'une fonction linéarisable H. Jellouli
11. Indice holomorphe et multiplicateur H. Jellouli
12. An alternative proof of Mañé's theorem on non-expanding Julia sets M. Shishikura and L.Tan
13. Geometry and dimension of Julia sets Y. -C. Yin
14. On a theorem of Mary Rees for the matings of polynomials M. Shishikura
15. Le théorème d'intégrabilité des structures presque complexes A. Douady and X. Buff
16. Bifurcation of parabolic fixed points M. Shishikura.
