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	Non disponible
ISBN 13	9780521337052
ISBN 10	0521337054
Titre	The Geometry of Fractal Sets
Auteur	K J Falconer
Série	Cambridge Tracts In Mathematics
État	Non disponible
Type de reliure	Paperback
Éditeur	Cambridge University Press
Année de publication	1986-07-24
Nombre de pages	180
Note de couverture	La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier.
Note	Non disponible