In this talk, we shall study about the leaking rate of the Sinai-Ruelle-Bowen (SRB) measure through holes of positive measure constructed 
 in the Julia set of hyperbolic rational maps (open dynamics). The dependence of this rate on the size and position of the hole shall be explained. 
 For an easier and better understanding, the simple quadratic map restricted on the unit circle will be analysed thoroughly. Time permitting, we 
 will also compute the Hausdorff dimension of the survivor set.