Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators

摘要

The chaotic and hypercyclic behavior of the C ₀-semigroups of operators generated by a perturbation of the Ornstein-Uhlenbeck operator with a multiple of the identity in is investigated. Negative and positive results are presented, depending on the signs of the real parts of the eigenvalues of the matrix appearing in the drift of the operator.