Finite automata were used to determine multiple addresses in number systems and to find
topological properties of self-affine tiles and finite type fractals. We join these two lines of …

Let $ B^{\sigma} _ {2,\infty} $ denote the Besov space defined on a compact set $ K\subset
{\Bbb R}^ d $ which is equipped with an $\alpha $-regular measure $\mu $. The critical …

Sierpinski gasket Page 1 J. Fractal Geom. 5 (2018), 419–42 DOI 10.4171/JFG/66 Journal of
Fractal Geometry © European Mathematical Society Determination of the walk dimension of …

Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov
hyperbolic graph on the IFS has been established recently. In the paper, we introduce a …

We describe the set of all Dirichlet forms associated to a given infinite graph in terms of
Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form …

In a previous paper [arxiv: 1604.05440], we studied certain random walks on the hyperbolic
graphs $ X $ associated with the self-similar sets $ K $, and showed that the discrete energy …

Let Γ n denote the n-th level Sierpiński graph of the Sierpiński gasket K. We consider, for any
given conductance (a 0, b 0, c 0) on Γ 0, the Dirichlet form E on K obtained from a recursive …

Resistance estimates and critical exponents of Dirichlet forms on fractals Page 1 Qingsong
Gu and Ka-Sing Lau Resistance estimates and critical exponents of Dirichlet forms on fractals …

It is well known that for a Brownian motion, if we change the medium to be inhomogeneous
by a measure μ, then the new motion (the time-changed process) will diffuse according to a …

We consider a class of infinite weighted metric trees obtained as perturbations of self‐similar
regular trees. Possible definitions of the boundary traces of functions in the Sobolev space …