ENGLISH

The geometry of fractal sets

By K. J. Falconer

Book information

Publisher
CUP
Year
1985
ISBN
9780521337052, 0521337054
Open Library ID
OL15058466M
Language
english
Format
DJVU
Filesize
1 MB (1383868 bytes)
Series
Cambridge Tracts in Mathematics
Pages
177\177
Library
Kolxo3
DPI
300
Time added
2010-11-11 16:01:50

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.

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