On the union of homogeneous symmetric Cantor set with its translations

Derong Kong, Wenxia Li, Zhiqiang Wang +2

Fix a positive integer $N$ and a real number $0<\beta <1/(N+1)$. Let $\Gamma$ be the homogeneous symmetric Cantor set generated by the IFS $$ \Big\{ ϕ_i(x)=βx + i \frac{1-β}{N}: i=0,1,\cdo…