The Geometry of Fractal Sets
The Geometry of Fractal Sets
Regular price
Checking stock...
Regular price
Checking stock...
Summary
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.
The feel-good place to buy books
- Free delivery in Ireland
- Supporting authors with AuthorSHARE
- 100% recyclable packaging
- Proud to be a B Corp – A Business for good
- Buy-back with Ziffit
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 |