论文信息 - Dirichlet forms on non-self-similar fractals: Hanoi attractors - 字舞流文

Dirichlet forms on non-self-similar fractals: Hanoi attractors

We present the construction of a local and regular Dirichlet form on the so-called Hanoi attractor of parameter α for any α ∈ (0, 1 / 3). Since these fractals are non-self-similar sets, we need to modify the classical construction of Kigami et al.

Uta Freiberg | Patricia Alonso-Ruiz

[1] M. Okada,et al. Heat kernels on infinite graph networks and deformed Sierpinski gaskets , 1990 .

[2] S. Klavžar,et al. Graphs S(n, k) and a Variant of the Tower of Hanoi Problem , 1997 .

[3] Uta Freiberg,et al. Energy Form on a Closed Fractal Curve , 2004 .

[4] W. Rudin. Real and complex analysis , 1968 .

[5] M. R. Lancia,et al. Energy forms on conformal C1‐diffeomorphic images of the Sierpinski gasket , 2008 .

[6] James Tanton. Mathematics Galore!: The Tower of Hanoi , 2012 .

[7] Patricia Alonso-Ruiz,et al. Dirichlet forms on non self-similar sets : Hanoi attractors and the Sierpiński gasket , 2013 .

[8] J. Kigami,et al. Analysis on Fractals , 2001 .

[9] Patricia Alonso-Ruiz,et al. Hanoi attractors and the Sierpiński gasket , 2012, Int. J. Math. Model. Numer. Optimisation.

[10] Jun Kigami,et al. A harmonic calculus on the Sierpinski spaces , 1989 .

[11] A. M. Hinz,et al. The average distance on the Sierpiński gasket , 1990 .

[12] Robert S. Strichartz,et al. Differential Equations on Fractals: A Tutorial , 2006 .

[13] S. Goldstein. Random Walks and Diffusions on Fractals , 1987 .

[14] Martin T. Barlow,et al. Brownian motion on the Sierpinski gasket , 1988 .

[15] Jun Kigami,et al. Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals , 1993 .

[16] S. Kusuoka,et al. Dirichlet forms on fractals and products of random matrices , 1989 .