The Geometry of Fractal Sets
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Geometry of Fractal Sets by Kenneth J. Falconer
Book DescriptionThis 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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Book DetailsISBN: 9780521337052
(228mm x 152mm x 11mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Jul-1986
Country of Publication: United Kingdom
Books By Author Kenneth J. Falconer
Fractal Geometry, Hardback (January 2014)
This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science.
Fractals: A Very Short Introduction, Paperback (September 2013)
From the contours of coastlines to the outlines of clouds, fractal shapes can be found regularly in nature. This Very Short Introduction explains the basic concepts, presents the 'new geometry' of fractals, explores its wide range of applications, and shows the central place fractals have gained in mathematics and science in recent years.
Techniques in Fractal Geometry, Hardback (March 1997)» View all books by Kenneth J. Falconer
Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals. Much of the material presented in this book has come to the fore in recent years.
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