The Geometry of Fractal Sets by K J Falconer

The Geometry of Fractal Sets by K J Falconer

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.

'This book is filled with the geometric jewels of fractional and integral Hausdorff dimensionIt contains a much-needed unified notation and includes many recent results with simplified proofs. The theory is classically and rigorously presented with applications only alluded to in the introduction. Each chapter contains a short and important problem set. This is a lovely introduction to the mathematics of fractal sets for the pure mathematician.' American Mathematical Monthly

SKU	Unavailable
ISBN 13	9780521337052
ISBN 10	0521337054
Title	The Geometry of Fractal Sets
Author	K J Falconer
Series	Cambridge Tracts In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Cambridge University Press
Year published	1986-07-24
Number of pages	180
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable