Asymptotics for the spectral and walk dimension as fractals approach Euclidean space

B. M. Hambly*, T. Kumagai

*この研究の対応する著者

研究成果: Article査読

9 被引用数 (Scopus)

抄録

We discuss the behavior of the dynamic dimension exponents for families of fractals based on the Sierpinski gasket and carpet. As the length scale factor for the family tends to infinity, the lattice approximations to the fractals look more like the tetrahedral or cubic lattice in Euclidean space and the fractal dimension converges to that of the embedding space. However, in the Sierpinski gasket case, the spectral dimension converges to two for all dimensions. In two dimensions, we prove a conjecture made in the physics literature concerning the rate of convergence. On the other hand, for natural families of Sierpinski carpets, the spectral dimension converges to the dimension of the embedding Euclidean space. In general, we demonstrate that for both cases of finitely and infinitely ramified fractals, a variety of asymptotic values for the spectral dimension can be achieved.

本文言語English
ページ(範囲)403-412
ページ数10
ジャーナルFractals
10
4
DOI
出版ステータスPublished - 2002 12月
外部発表はい

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 幾何学とトポロジー
  • 応用数学

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