Genericity of wild holomorphic functions and common hypercyclic vectors

Let T, be the translation operator by a in the space of entire functions K(C) defined by T-alpha (f) (z) = f (z + alpha). We prove that there is a residual set G of entire functions such that for every f is an element of G and every alpha is an element of C\{0} the sequence T-alpha(n)(f) is dense in K(C), that is, G is a residual set of common hypercyclic vectors (functions) for the family {T-alpha : alpha is an element of C\{0}}. Also, we prove similar results for many families of operators as: multiples of differential operator, multiples of backward shift, weighted backward shifts. (C) 2003 Elsevier Science (USA). All rights reserved.