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Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on thermodynamic, ergodic and fractal properties of these functions (notably, equilibrium states, Bowen's formula and Sullivan's conformal measures). This volume builds on the first two volumes in the series while simultaneously developing some methods and techniques specific to rational functions.

Dynamic systems, fractal geometry, thermodynamic formalism, and Riemann sphere.

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Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame-a close collaborator with Benoit Mandelbrot, the founder of fractal geometry-and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.

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

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

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

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International authorities from Canada, Denmark, England, Germany, Russia and South Africa focus on research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysis. They address the rich panoply of manifold applications of fractal geometry available for study and research in science and industry: i.e., remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis. Economically priced, this important and authoritative reference source for research and study cites o

Geometry. --- Fractals. --- Mathematics. --- Math --- Science --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Mathematics --- Euclid's Elements