1 citations · 3 across the 8 of their papers we have counts for
8 papers
Sub-self-similar sets with distinct Hausdorff and Box dimensions
Junda Zhang
We construct an IFS consisting of three contracting similarities on with a countable compact sub-self-similar set with distinct Hausdorff and lower box dimensi…
On the minimal generating weighted IFS of self-similar measure
Junda Zhang
We concern the structure of generating weighted IFSs of a self-similar measure on the real line. We provide various sufficient conditions for the existence of a minimal generating…
A positive answer to a symmetry conjecture on homogeneous IFS
Junda Zhang
If two homogeneous IFSs satisfying the OSC with opposite common contraction factors share the same attractor on the real line, we show that this attractor is symmetric. This answer…
Algebraic dependence number and cardinality of generating iterated function systems
Junda Zhang
For a dust-like self-similar set (generated by IFSs with the strong separation condition), Elekes, Keleti and Máthé found an invariant, called `algebraic dependence number', by con…
Besov-Lipschitz norm and -energy measure on scale-irregular Vicsek sets
Aobo Chen, Jin Gao, Zhenyu Yu +1
In this paper, we establish the existence of -energy norms and the corresponding -energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also inv…
Weak monotonicity property of Korevaar-Schoen norms on nested fractals
Diwen Chang, Jin Gao, Zhenyu Yu +1
In this paper, we study the weak monotonicity property of p-energy related Korevaar-Schoen norms on connected nested fractals for . Such property has many important…
Heat kernel-based p-energy norms on metric measure spaces
Jin Gao, Zhenyu Yu, Junda Zhang
We investigate heat kernel-based and other -energy norms (1<p<\infty) on bounded and unbounded metric measure spaces, in particular, on nested fractals and their blowups. With t…
A dichotomy on the self-similarity of graph-directed attractors
Kenneth J. Falconer, Jiaxin Hu, Junda Zhang
This paper seeks conditions that ensure that the attractor of a graph directed iterated function system (GD-IFS) cannot be realised as the attractor of a standard iterated function…