Distributional chaos for strongly continuous semigroups of operators
Angela A. Albanese Xavier Barrachina Elisabetta M. Mangino Alfredo Peris
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.
keywords: Distributional chaos hypercyclic operators irregular vectors criterion for distributional chaos. $C_0$-semigroups
Chaotic translation semigroups
José A. Conejero Alfredo Peris
We characterize chaos for the translation semigroup, with a sector in the complex plane as index set, defined on a weighted function space. The results are stated in terms of the integrability of the weight function, and in terms of the existence of periodic points. We generalize previous results of [8, 15]. Some examples are also provided to complete the study.
keywords: Chaotic semigroups of operators.
Hypercyclic translation $C_0$-semigroups on complex sectors
José A. Conejero Alfredo Peris
We study the hypercyclic behaviour of sequences of operators in a $C_0$-semigroup whose index set is a sector in the complex plane. The hypercyclicity and chaos for the concrete case of the translation semigroup is analyzed. Some examples are provided to complete the results.
keywords: infinite-dimensional linear systems translation semigroup. topological transitivity topologically mixing Chaotic semigroup hypercyclic semigroup

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