Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals.

Much of the material presented in this book has come to the fore in recent years. This includes methods for studying dimensions and other parameters of fractal sets and measures, as well as more sophisticated techniques such as thermodynamic formalism and tangent measures. In addition to general theory, many examples and applications are described, in areas such as differential...

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse...

When originally published, this text was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. The first of the three chapters contains an introduction to measure theory, paying particular attention to the study of non-sigma-finite measures. The second chapter develops the most general aspects of the theory of Hausdorff measures, and the final chapter gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This new edition has a foreword by Kenneth Falconer...

This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science. New research developments are highlighted, such as porosity, while covering other much more sophisticated topics, such as fractal aspects of conformal invariance, complex dimensions, and non-commutative fractal geometry. The book emphasizes dimension in its various...

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.