Lipschitz equivalence of a class of general Sierpinski carpets
نویسندگان
چکیده
منابع مشابه
The Hausdorff Dimension of General Sierpinski Carpets
We refer to R as a general Sierpίήski carpet, after Mandelbrot [4], since Sierpiήski's universal curve is a special case of this construction [6]. It is clear that R = {J[fi(R)9 where r = \R\ and the ft are affine maps contracting R by a factor of n horizontally and m vertically. When n = m these maps are actually similarity transformations, and a well known argument shows the dimension of R is...
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Article history: Received 26 October 2007 Available online 10 July 2008 Submitted by M. Laczkovich
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We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined. Research partially supported by NSERC (Canada), and EPSRC (UK). Research partially...
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We consider a random version of the McMullen–Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an applica...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.06.018