Distributional chaos for strongly continuous semigroups of operators

Angela A. Albanese; Xavier Barrachina; Elisabetta M. Mangino; Alfredo Peris

doi:10.3934/cpaa.2013.12.2069

Article Contents

2013, Volume 12, Issue 5: 2069-2082. Doi: 10.3934/cpaa.2013.12.2069

This issue Previous Article Asymptotically periodic solutions of neutral partial differential equations with infinite delay Next Article The sign of the wave speed for the Lotka-Volterra competition-diffusion system

Distributional chaos for strongly continuous semigroups of operators

1.
Department of Mathematics “E. De Giorgi”, University of Salento, P.O. Box 193, Via Per Arnesano, 73100 Lecce
2.
Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Edifici 8E, 46022 València
3.
Dipartimento di Matematica e Fisica "Ennio De Giorgi'', Università del Salento, Via Per Arnesano P.O. Box 193, 73100 Lecce
4.
Departament de Matemàtica Aplicada & IUMPA Edifici 7A, Universitat Politècnica de València, E-46022, València

Received: January 31, 2012

Revised: September 30, 2012

Published: August 2013

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Abstract

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.

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Mathematics Subject Classification: 47A16, 47D06, 37D45.

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