D-Hypercyclic and d-chaotic properties of abstract differential equations of first order

Abstract

The main aim of this paper is to contribute to the existing the- ory of disjoint hypercyclic and disjoint topologically transitive abstract non- degenerate differential equations of first order as well as to initiate the study of disjoint chaoticity for strongly continuous semigroups and C-distribution semigroups in Banach and Fr ́echet function spaces. We also investigate dis- joint topologically mixing property for C-distribution semigroups, and prove a disjoint analogue of the Desch-Schappacher-Webb criterion in this context. Some new results on disjoint transitivity and disjoint chaoticity of strongly con- tinuous families of composition operators and strongly continuous semigroups induced by semiflows are shown, as well.