The-Hausdorff-dimension-of-the-survivor-set

Rui Kuang, Bing Li, Yuanfen Xiao

Let $1<\beta <2$, the sequence $\alpha (\beta )=\alpha (\beta {)}_1\alpha (\beta {)}_2\cdots$ be the quasi-greedy $\beta$-expansion of $1$, and $t\in [0,1)$ be a bifurcation parameter. The $\beta$-transformation is define…