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1.
Robert S. Strichartz 《Proceedings of the American Mathematical Society》2002,130(3):805-817
Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.
2.
本文考察了包括平面上的各种广义 Cantor集 ,Sierpinski集和包括某些连续不可微曲线在内的广义 Sierpinski集 .由相似变换 ,导出了它们的级数表达式 ,并利用它和字符串空间的对应关系 ,计算出它们的Hausdorff维数 相似文献
3.
Marion SCHEEPERS 《数学学报(英文版)》2007,23(7):1153-1162
We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property. 相似文献
4.
吴炯圻 《纯粹数学与应用数学》2003,19(3):206-212
在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM. 相似文献
5.
We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimensiond. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimensiond. 相似文献
6.
I. McGillivray 《Potential Analysis》2002,16(3):289-303
We study the effective resistance between disjoint compact sets relative to the n-th level approximation F
n
to the generalized Sierpiski carpet in d dimensions. This yields a simple criterion for determining recurrence of simple random walk on the associated pre-fractal graph in terms of the resistance scaling factor. 相似文献
7.
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field. 相似文献
8.
Can a Brownian motion penetrate the two-dimensional Sierpinski gasket? This question was studied in [8], and an affirmative answer was given. In this paper, the problem is studied with a different approach, using Dirichlet forms and function space theory. The results obtained are somewhat different from, and from certain aspects more general than, the results in [8].
相似文献9.
Let {X(t),t≥0} be Brownian motion on Sierpinski gasket,The Hausdorff and packing dimensions of the image of a ompact set are studied,The uniform Hausdorff and packing dimensions of the inverse image are also discussed. 相似文献
10.
Tetsuya Hattori 《Journal of statistical physics》2007,127(3):609-627
Let W(x,y) = ax
3+ bx
4+ f
5
x
5+ f
6
x
6+ (3 ax
2)2
y+ g
5
x
5
y + h
3
x
3
y
2 + h
4
x
4
y
2 + n
3
x
3
y
3+a
24
x
2
y
4+a
05
y
5+a
15
xy
5+a
06
y
6, and X = , , where the coefficients are non-negative constants, with a > 0, such that X
2(x,x
2)−Y(x,x
2) is a polynomial of x with non-negative coefficients.
Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding
paths on the 3 and 4 dimensional pre-gaskets.
We prove that there exists a unique fixed point (x
f
,y
f
) of Φ in the invariant set .
2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41. 相似文献