The Hausdorff Dimension Of A Class Of Sub-cookie-cutter Sets

In this paper we introduce the definitions of cookie-cutter sets and sub-cookie-cutter sets, describe the generation of sub-cookie-cutter sets and give a method to calculate the Hausdorff dimension of a class of sub-cookie-cutter sets. By using the Gibbs measure and pressure function we obtain the exact formula of Hausdorff dimensions of these sub-cookie-cutter sets and the symbols sets which generate them. The Hausdorff dimensions of sub-cookie-cutter sets and the corresponding symbols sets are equal.