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Hypercyclic semigroups generated by Ornstein-Uhlenbeck operators. (English) Zbl 1215.47012
In this paper, the authors discuss the hypercyclicity and supercyclicity of semigroups generated by Ornstein-Uhlenbeck operators. They show that, under certain conditions, the semigroup is chaotic for the one-dimensional model, otherwise, it is supercyclic but not hypercyclic. For the multi-dimensional case, they obtain similar results.
MSC:
47A16Cyclic vectors, hypercyclic and chaotic operators
47D06One-parameter semigroups and linear evolution equations
47D07Markov semigroups of linear operators and applications to diffusion processes
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