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The Geometry of Fractal Sets (Cambridge Tracts in Mathematics, S
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Item specifics
- Condition
- Title
- The Geometry of Fractal Sets (Cambridge Tracts in Mathematics, S
- ISBN
- 9780521337052
- Publication Name
- Geometry of Fractal Sets
- Item Length
- 9in
- Publisher
- Cambridge University Press
- Publication Year
- 1986
- Series
- Cambridge Tracts in Mathematics Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Height
- 0.4in
- Item Width
- 6.1in
- Item Weight
- 9.5 Oz
- Number of Pages
- 180 Pages
About this product
Product Information
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.
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
0521337054
ISBN-13
9780521337052
eBay Product ID (ePID)
394788
Product Key Features
Publication Name
Geometry of Fractal Sets
Format
Trade Paperback
Language
English
Publication Year
1986
Series
Cambridge Tracts in Mathematics Ser.
Type
Textbook
Number of Pages
180 Pages
Dimensions
Item Length
9in
Item Height
0.4in
Item Width
6.1in
Item Weight
9.5 Oz
Additional Product Features
Series Volume Number
Series Number 85
Lc Classification Number
Qa447 1986
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
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.
Target Audience
Scholarly & Professional
Topic
Geometry / Differential, Set Theory, Mathematical Analysis
Dewey Decimal
515/.64
Dewey Edition
19
Illustrated
Yes
Genre
Mathematics
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