This volume presents 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. Chapters document important results hitherto unpublished or difficult to find in the literature.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 to researchers in dynamical systems and Kleinian groups.
Inhaltsverzeichnis
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.
