A notion of Euler characteristic for fractals

by    Marta Llorente, Steffen Winter

Preprint series: 04-04, Reports on Analysis and Algebra and Geometry

28A80 Fractals [See also 37Fxx]
52A38 Length, area, volume [See also 26B15, 28A75, 49Q20]

Abstract: A notion of (average) fractal Euler number for subsets in the Euclidean space with infinite singular complexes is introduced by means of rescaled Euler numbers of infinitesimal r-neighbourhoods. For certain classes of self-similar sets we calculate the associated Euler exponent and the (average) fractal Euler number with the help of the renewal theorem. Examples like the Sierpinski
gasket or carpet are provided.

Keywords: Euler characteristic, fractal, complexes.

Upload: 2004-03-04

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