This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.…mehr
This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.
Preface.- Introduction.- Part 1: Geometric Measure Theory.- Sixty Years of Fractal Projections.- Scenery flow, conical densities, and rectifiability.- The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals.- Projections of self-similar and related fractals: a survey of recent developments.- Part 2: Self-similar Fractals and Recurrent Structures.- Dimension of the graphs of the Weierstrass-type functions.- Tiling Z2 by a set of four elements.- Some recent developments in quantization of fractal measures.- Apollonian Circle Packings.- Entropy of Lyapunov-optimizing measures of some matrix cocycles.- Part 3: Analysis and Algebra on Fractals.- Poincaré functional equations, harmonic measures on Julia sets, and fractal zeta functions.- From self-similar groups to self-similar sets and spectra.- Finite energy coordinates and vector analysis on fractals.- Fractal zeta functions and complex dimensions: A general higher-dimensional theory.- Part 4: Multifractal Theory.- Inverse problems in multifractal analysis.- Multifractal analysis based on p-exponents and lacunarity exponents.- Part 5: Random Constructions.- Dimensions of Random Covering Sets.- Expected lifetime and capacity.
Preface.- Introduction.- Part 1: Geometric Measure Theory.- Sixty Years of Fractal Projections.- Scenery flow, conical densities, and rectifiability.- The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals.- Projections of self-similar and related fractals: a survey of recent developments.- Part 2: Self-similar Fractals and Recurrent Structures.- Dimension of the graphs of the Weierstrass-type functions.- Tiling Z2 by a set of four elements.- Some recent developments in quantization of fractal measures.- Apollonian Circle Packings.- Entropy of Lyapunov-optimizing measures of some matrix cocycles.- Part 3: Analysis and Algebra on Fractals.- Poincaré functional equations, harmonic measures on Julia sets, and fractal zeta functions.- From self-similar groups to self-similar sets and spectra.- Finite energy coordinates and vector analysis on fractals.- Fractal zeta functions and complex dimensions: A general higher-dimensional theory.- Part 4: Multifractal Theory.- Inverse problems in multifractal analysis.- Multifractal analysis based on p-exponents and lacunarity exponents.- Part 5: Random Constructions.- Dimensions of Random Covering Sets.- Expected lifetime and capacity.
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