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A notion of Euler characteristic for fractals
Marta Llorente and Steffen WinterAbstract
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.
- Received:
- 14.05.04
- Published:
- 14.05.04
- MSC Codes:
- 28A80, 52A38, 26B15
- Keywords:
- euler characteristic, self-similar sets, renewal theorem