3 papers
math.CA2024
Self-embedding similitudes of Bedford-McMullen carpets with dependent ratios
Jian-Ci Xiao
We prove that any non-degenerate Bedford-McMullen carpet does not admit oblique self-embedding similitudes; that is, if is a similitude sending the carpet into itself, then the…
math.GN2024
A self-similar set with non-locally connected components
Jian-Ci Xiao
Luo, Rao and Xiong [Topol. Appl. 322 (2022), 108271] conjectured that if a planar self-similar iterated function system with the open set condition does not involve rotations or re…
math.DS2023
On a self-embedding problem of self-similar sets
Jian-Ci Xiao
Let be a self-similar set generated by an iterated function system satisfying the strong separation condition and let be a contracting…