Dimension spectra of self-affine sets

被引：0
|
作者：
Satoshi Takahashi
机构：
[1] Nara Women’s University,Graduate School of Human Culture
来源：
Israel Journal of Mathematics | 2002年 / 127卷
关键词：
Free Energy; Hausdorff Dimension; Gibbs Measure; Variational Formula; Legendre Transformation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The dimension spectrumH(δ) is a function characterizing the distribution of dimension of sections. Using the multifractal formula for sofic measures, we show that the dimension spectra of irreducible self-affine sets (McMullen’s Carpet) coincide with the modified Legendre transform of the free energy Ψd(β). This variational relation leads to the formula of Hausdorff dimension of self-affine sets, max(δ +H(δ)) = Ψd(η), whereη is the logarithmic ratio of the contraction rates of the affine maps.
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页码：1 / 17
页数：16
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