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Mandelbrot, B.

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Mandelbrot, Benoit B

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This book is devoted to the structure of the Mandelbrot set - a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory. The Mandelbrot set is one of the bridges connecting the world of chaos and order. The authors restrict consideration to discrete dynamics of a single variable. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism. The coverage

Mandelbrot sets. --- Molecules, Mu --- Mu molecules --- Sets, Mandelbrot --- Fractals

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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 In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature.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.

Mandelbrot sets. --- Fractals. --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Molecules, Mu --- Mu molecules --- Sets, Mandelbrot --- Fractals --- Mandelbrot sets

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Mathematicians --- Mathématiciens --- Mélanges (Recueils) --- Géométrie. --- Fractales. --- Modèles mathématiques. --- Mandelbrot, Benoit B. --- Mandelbrot, Benoit B.