Polynomial automorphisms and hypercyclic operators on spaces of analytic functions

Abstract

We consider hypercyclic composition operators on H(Cn) which can be obtained from the translation operator using polynomial automorphisms of Cn. In particular we show that if CS is a hypercyclic operator for an affine automorphism S on H(Cn), then S = Θ◦ (I +b) ◦Θ−1 +a for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of ‘‘symmetric translations’’ on a space of symmetric analytic functions on l1.