2 citations · 2 across the 4 of their papers we have counts for
4 papers
Finite state automata and homeomorphism of self-similar sets
Liangyi Huang, Zhiying Wen, Yamin Yang +1
The topological and metrical equivalence of fractals is an important topic in analysis. In this paper, we use a class of finite state automata, called -automaton, to construct p…
Box-counting measure of metric spaces
Liang-yi Huang, Hui Rao, Zhiying Wen +1
In this paper, we introduce a new notion called the \emph{box-counting measure} of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a…
Relations between topological and metrical properties of self-affine Sierpiski sponges
Yuan Zhang, Liang-Yi Huang
We investigate two Lipschitz invariants of metric spaces defined by -connected components, called the maximal power law property and the perfectly disconnectedness. The first pr…
A dimension drop phenomenon of fractal cubes
Liangyi Huang, Hui Rao
Let E be a metric space. We introduce a notion of connectedness index of E, which is the Hausdor? dimension of the union of non-trivial connected components of E. We show that the…