Distributional chaos for strongly continuous semigroups of operators

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 chaos on the point spectrum of the generator of the semigroup is presented. An application to the semigroup generated in L-2 (R) by a translation of the Ornstein-Uhlenbeck operator is also given.This work is supported in part by MEC and FEDER, Project MTM2010-14909, by Generalitat Valenciana, Projects PROMETEO/2008/101 and GV/2010/091, and by Universitat Politecnica de Valencia, Project PAID-06-0-92932. The second author also wants to acknowledge the support of the Project PAID-00-10 and of the grant FPI-UPV2009-04 from Programa de Ayudas de Investigacion y Desarrollo de la Universitat Politecnica de Valencia.Albanese, AA.; Barrachina Civera, X.; Mangino, EM.; Peris Manguillot, A. (2013). Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis. 12(5):2069-2082. https://doi.org/10.3934/cpaa.2013.12.2069S2069208212