The Entropy of Cantor--like measures

By a Cantor-like measure we mean the unique self-similar probability measure $\mu$ satisfying $\mu =\sum_{i=0}^{m-1}p_{i}\mu \circ S_{i}^{-1}$ where $$ for integers $2\leq d<m\le 2d-1$ and probabilities $p_{i}>0$, $\sum p_{i}=1$. In the uniform case ($p_{i}=1/m$ for all $i$) we show how one can compute the entropy and Hausdorff dimension to arbitrary precision. In the non-uniform case we find bounds on the entropy.