The Mandelbrot Set, Theme and Variations, Issue 274Tan Lei 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 In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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. |
Contents
GEOMETRY AND DIMENSION OF JULIA SETS | 281 |
On a theorem of M Rees for matings of polynomials | 289 |
Le théoreme dintégrabilité des structures presque complexes | 307 |
BIFURCATION OF PARABOLIC FIXED POINTS | 325 |
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analytiquement B(zo branched covering compact set component constant contains continuous convergence cqfd critical point D'après décroissance rapide defined degenerate mating denote depending diam difféomorphisme Douady dynamics Ecalle cylinders exists extend external rays F₁ f₂ Fatou coordinates fixed point fo E Fo fo(z follows formal mating function fundamental regions h₂ Hence holomorphe holomorphic functions homeomorphism homotopic immediate parabolic basin injective integer Julia set l'équation de Beltrami l'infini Lemma lemme Let F Main Theorem Mandelbrot set Möbius transformation Moreover neighborhood ouvert parabolic fixed point parabolic periodic points perturbation polynomials Posons Proof Proposition 2.5.2 Proposition 3.2.3 R₁ rational map ray-equivalence resp return map satisfies semi-conjugacy sens des distributions simply connected spherical metric Suppose tend vers Tƒ(w Thurston equivalent Thurston's type topology tout transition map U₁ univalent voisinage W₁ მი