On the Minkowski measurability of self-similar fractals in R-d

Creative Commons License

DENİZ A., KOÇAK M. Ş., Ozdemir Y., Ratiu A., Ureyen A. E.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.5, pp.830-846, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1103-20
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.830-846
  • Keywords: Self-similar fractals, Minkowski measurability, tube formulas, TUBE FORMULAS, TILINGS
  • Anadolu University Affiliated: Yes

Abstract

The question of Minkowski measurability of fractals is investigated for different situations by various authors, notably by M. Lapidus. In dimension one it is known that the attractor of an IFS consisting of similitudes (and satisfying a certain open set condition) is Minkowski measurable if and only if the IFS is of non-lattice type and it was conjectured that this would be true also in higher dimensions. Half of this conjecture was proved by Gatzouras in 2000, who showed that the attractor of an IFS (satisfying the open set condition) is Minkowski measurable if the IFS is of non-lattice type.