On the structure of $\lambda$-Cantor set with overlaps

Karma Dajani, Derong Kong, Yuanyuan Yao

Given $\lambda \in (0,1)$, let $E_{\lambda }$ be the self-similar set generated by the iterated function system $\{x/3,(x+\lambda )/3,(x+2)/3\}$. Then $E_{\lambda }$ is a self-similar set with overlaps. We obtain…