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Distributional chaos for strongly continuous semigroups of operators. (English) Zbl 06160520
The authors study and characterize distributional chaos for strongly continuous semigroups of bounded linear operators on Banach spaces. They show that distributional chaos is equivalent to the existence of a distributionally irregular vector. They give a sufficient condition for distributional chaos on the point spectrum of the generator of the semigroup and they also give an application to the semigroup generated in ${L}^{2}\left(ℝ\right)$ by a translation of the Ornstein-Uhlenbeck operator.
##### MSC:
 47A16 Cyclic vectors, hypercyclic and chaotic operators 47D06 One-parameter semigroups and linear evolution equations 37D45 Strange attractors, chaotic dynamics