The geometry of fractal sets

Description

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 examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

Subjects

Series Statement

• Cambridge tracts in mathematics ;

Other Editions

• The geometry of fractal setsCambridge University Press1985-01-01
• The geometry of fractal sets.Cambridge University Press1986-01-01
• Geometry of Fractal SetsCambridge University Press2010-01-01
• Geometry of Fractal SetsCambridge University Press2011-01-01