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Self-similar sets and measures
Graf, Siegfried
1994
Abstract
A major theme in the theory of fractals is that of self—similarity: the whole fractal set is composed of smaller parts which are geometrically similar to whole set. There are several ways to formulate this concept in a mathematically rigorous way. Неге I will deal with Hutchinson’s definition of self-similarity. It is the purpose of this lecture to collect some of the basic results concerning the Hausdorff dimension, Hausdorff measure and local structure of self-similar sets and measures. I am not striving for completeness but rather use my own research interests as a guide to the results and problems in the area. Most of the proofs are omitted. Interested roaders are refered to the literature.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
26 (1994) suppl.
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Siegfried Graf, "Self-similar sets and measures", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 26 (1994) suppl., pp. 35-48.
Languages
en
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