Products of random matrices and derivatives on p.c.f. fractals
Products of random matrices and derivatives on p.c.f. fractals
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DOI：
10.1016/j.jfa.2007.12.001
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发表时间：
2008-03
影响因子：
1.7
通讯作者：
Anders Pelander;A. Teplyaev
中科院分区：
文献类型：
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作者：
Anders Pelander;A. Teplyaev
我们定义并研究了后临界有限分形的内在一阶导数，并证明了对于某些类别的分形和函数的自相似测度几乎处处的可微性。我们应用我们的结果将“地理就是命运”原理扩展到这些情况，并且还获得了 Sierpiński 垫片上局部偏心率的逐点行为的结果，这是 Öberg、Strichartz 和 Yingst 以及作者之前研究的结果。我们还建立了导数与 Strichartz 和作者之前研究的切线和梯度的关系。我们的主要工具是随机矩阵乘积的 Furstenberg-Kesten 理论。
We define and study intrinsic first order derivatives on post critically finite fractals and prove differentiability almost everywhere with respect to self-similar measures for certain classes of fractals and functions. We apply our results to extend the geography is destiny principle to these cases, and also obtain results on the pointwise behavior of local eccentricities on the Sierpiński gasket, previously studied by Öberg, Strichartz and Yingst, and the authors. We also establish the relation of the derivatives to the tangents and gradients previously studied by Strichartz and the authors. Our main tool is the Furstenberg–Kesten theory of products of random matrices.