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The geometry of fractal sets

Falconer, K. J., (1952-)

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The geometry of fractal sets

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The geometry of fractal sets/ K.J. Falconer.
作者:	Falconer, K. J.,
出版者:	Cambridge :Cambridge University Press, : 1985.,
面頁冊數:	xiv, 162 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Fractals. -
電子資源:	https://doi.org/10.1017/CBO9780511623738
ISBN:	9780511623738

The geometry of fractal sets
Falconer, K. J.,1952-

The geometry of fractal sets[electronic resource] /K.J. Falconer. - Cambridge :Cambridge University Press,1985. - xiv, 162 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;85. - Cambridge tracts in mathematics ;85..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511623738Subjects--Topical Terms:

524457
Fractals.

LC Class. No.: QA248 / .F274 1985

Dewey Class. No.: 515.64

The geometry of fractal sets
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a 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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