Periods of strongly continuous semigroups

Abstract

In this paper, we study the set of periods of (chaotic) strongly continuous semigroups. We prove a relationship between eigenvalues on the imaginary axis of the generator of a strongly continuous semigroup and the set of periods of the semigroup itself. This relationship in turn is used to obtain information about the structure of the set of periods and to construct (chaotic) semigroups with prescribed periods.