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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…