Transfer operator and conformal measures for a class of maps having covering property

Let $(X,d)$ be a metric space and $X_0$ be an open and dense subset of $X$. We develop the Walters' theory and discuss the existence of conformal measures in terms of the Perron-Frobenius-Ruelle operator for a continuous map $T:X_0\rightarrow X$ and the Bowen formula about Hausdorff dimension and Poincar\'e exponent of some invariant subsests for $T$ with some expanding property.