The Mandelbrot set is a fractal shape that classifies the dynamics of quadratic polynomials. It has a remarkably rich geometric and combinatorial structure....
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Résumé
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 prescrits 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 In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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.
Sommaire
The Mandelbrot set is universal
Baby Mandelbrot sets are born in cauliflowers
Modulation dans l'ensemble de Mandelbrot
Local connectivity of Julia sets: expository lectures
Holomorphic motions and puzzles
Local properties of the Mandelbrot set at parabolic points
Convergence of rational rays in parameter spaces
Bounded recurrence of critical points and Jakobson's Theorem
The Herman-Swiatek Theorems with applications
Perturbation d'une fonction linéarisable
Indice holomorphe et multiplicateur
An alternative proof of Mañé's theorem on non-expanding Julia sets
Geometry and dimension of Julia sets
On a theorem of M Rees for the matings of polynomials
Le théorème d'intégrabilité des structures presque complexes