We consider digits-deleted sets or Cantor-type sets with $\beta$-expansions. We calculate the Hausdorff dimension $d$ of these sets and show that $d$ is continuous with respect to $\beta$. The $d$-dimentional Hausdorff measure of these sets is finite and positive.
Hausdorff dimension of boundaries of self-affine tiles in R^n
Hausdorff dimension of the set of points on divergent trajectories of a homogeneous flow on a product space
On the Hausdorff dimension of the escaping set of certain meromorphic functions
![QR code for arXiv:0706.4343 [math.DS]](http://oss.arxitics.com/images/favicon.svg)