On density and hypercyclicity

The aim of the paper ahead Birhoff , Maclane, Godefroy-Shapiro andKitai-Getner-Shapiro and the results of their theorems and hypercyclicoperators on space H(C). In Birhoffs theorem is shown that, if b isnon-zero, then the shift with the vector b is an hypercyclic operator.Maclane in 1952 showed that the Differentiation operator on H(C) isan hypercyclic operator. Bourdon and Shapiro also studied the behaviorof composition operators on this space.