✦ LIBER ✦

A notion of Euler characteristic for fractals

✍ Scribed by Marta Llorente; Steffen Winter

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 313 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410471

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A notion of (average) fractal Euler number for subsets of ℝ^d^ with infinite singular complexes is introduced by means of rescaled Euler numbers of infinitesimal ε ‐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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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