The recurrent hypercyclicity criterion for translation c0-semigroups on complex sectors

Let {Tt}t & ISIN; increment be the translation semigroup with a sector increment & SUB; C as index set. The recurrent hypercyclicity criterion (RHCC) for the C0-semigroup {Tt}t & ISIN; increment is established, and then the equivalent conditions ensuring {Tt}t & ISIN; increment satisfying the RHCC on weighted spaces of p-integrable and of continuous functions are presented. Especially, every chaotic semi -group {Tt}t & ISIN; increment satisfies the RHCC.