Geometry of Fractal Sets by K. J. Falconer pb

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ISBN
9780521337052
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Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521337054
ISBN-13
9780521337052
eBay Product ID (ePID)
394788

Product Key Features

Number of Pages
180 Pages
Publication Name
Geometry of Fractal Sets
Language
English
Publication Year
1986
Subject
Geometry / Differential, Set Theory, Mathematical Analysis
Type
Textbook
Author
K. J. Falconer
Subject Area
Mathematics
Series
Cambridge Tracts in Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Height
0.4 in
Item Weight
9.5 Oz
Item Length
9 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
TitleLeading
The
Dewey Edition
19
Reviews
‘This book is filled with the geometric jewels of fractional and integral Hausdorff dimension. It 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, "...a lovely introduction to the mathematics of fractal sets for the pure mathematician." American Mathematical Monthly, "...by far the most accessible mathematical account available and therefore is an invaluable addition to the literature." Science, 'This book is filled with the geometric jewels of fractional and integral Hausdorff dimension. It 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, 'This book is filled with the geometric jewels of fractional and integral Hausdorff dimension. It 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
Series Volume Number
Series Number 85
Illustrated
Yes
Dewey Decimal
515/.64
Table Of Content
Preface; Introduction; Notation; 1. Measure and dimension; 2. Basic density properties; 3. Structure of sets of integral dimension; 4. Structure of sets of non-integral dimension; 5. Comparable net measures; 6. Projection properties; 7. Besicovitch and Kakeya sets; 8. Miscellaneous examples of fractal sets; References; Index.
Synopsis
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 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.
LC Classification Number
QA447 1986

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