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

Authors: Patricia Alonso-Ruiz; Uta R. Freiberg

Addresses: Départment Mathematik, Emmy-Noether-Campus, Walter-Flex Straße 3, 57072 Siegen, Germany ' Départment Mathematik, Emmy-Noether-Campus, Walter-Flex Straße 3, 57072 Siegen, Germany

Abstract: 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.

Keywords: fractals; Dirichlet forms; diffusion processes; Laplacian; Sierpinski gasket; Hanoi graphs; Hanoi attractors; non-self-similar sets.

DOI: 10.1504/IJANS.2014.065150

International Journal of Applied Nonlinear Science, 2014 Vol.1 No.3, pp.247 - 274

Received: 28 Jan 2013
Accepted: 28 Jan 2013
Published online: 28 Oct 2014 *

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