We characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence ...
In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, ...
Albanese, Angela A.; Barrachina Civera, Xavier; Mangino, Elisabetta Maria; Peris Manguillot, Alfredo(American Institute of Mathematical Sciences (AIMS), 2013-09)
Distributional chaos for strongly continuous semigroups is studied and characterized. It is shown to be equivalent to the existence of a distributionally irregular vector. Finally, a sufficient condition for distributional ...