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

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

TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.5, ss.830-846, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 5
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3906/mat-1103-20
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.830-846
  • Anahtar Kelimeler: Self-similar fractals, Minkowski measurability, tube formulas, TUBE FORMULAS, TILINGS
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.