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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 () by a translation of the Ornstein-Uhlenbeck operator.
MSC:
47A16Cyclic vectors, hypercyclic and chaotic operators
47D06One-parameter semigroups and linear evolution equations
37D45Strange attractors, chaotic dynamics