D-Hypercyclic and d-chaotic properties of abstract differential equations of first order - C-C. Chen, M. Kostic, S. Pilipovic, D. Velinov (Department of Mathematics and Computer Sciences, Faculty of Science, Alexandria University, Alexandria, Egypt, 2018)
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.
Keywords: C-distribution semigroups, integrated C-semigroups, disjoint hyper- cyclicity, disjoint chaoticity, strongly continuous semigroups induced by semiflows, Frechet spaces.