Fractal Geometry and Stochastics V

✍ Scribed by Christoph Bandt, Kenneth Falconer, Martina Zähle (eds.)

• Publisher: Birkhäuser Basel
• Year: 2015
• Tongue: English
• Leaves: 339
• Series: Progress in Probability 70
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
Sixty Years of Fractal Projections....Pages 3-25
Scenery Flow, Conical Densities, and Rectifiability....Pages 27-38
The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals....Pages 39-52
Projections of Self-Similar and Related Fractals: A Survey of Recent Developments....Pages 53-74
Front Matter....Pages 75-75
Dimension of the Graphs of the Weierstrass-Type Functions....Pages 77-91
Tiling (\mathbb{Z}^{2}) by a Set of Four Elements....Pages 93-103
Some Recent Developments in Quantization of Fractal Measures....Pages 105-120
Apollonian Circle Packings....Pages 121-142
Entropy of Lyapunov-Optimizing Measures of Some Matrix Cocycles....Pages 143-154
Front Matter....Pages 155-155
Poincaré Functional Equations, Harmonic Measures on Julia Sets, and Fractal Zeta Functions....Pages 157-174
From Self-Similar Groups to Self-Similar Sets and Spectra....Pages 175-207
Finite Energy Coordinates and Vector Analysis on Fractals....Pages 209-227
Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory....Pages 229-257
Front Matter....Pages 259-259
Inverse Problems in Multifractal Analysis....Pages 261-278
Multifractal Analysis Based on p-Exponents and Lacunarity Exponents....Pages 279-313
Front Matter....Pages 315-315
Dimensions of Random Covering Sets....Pages 317-325
Expected Lifetime and Capacity....Pages 327-340
Back Matter....Pages 341-341

✦ Subjects

Probability Theory and Stochastic Processes; Geometry; Measure and Integration