Frequent hypercyclicity for translation C₀-semigroups on weighted spaces of continuous functions is studied. The results are achieved by establishing an analogy between frequent hypercyclicity for translation semigroups and for weighted pseudo-shifts and by characterizing frequently hypercyclic weighted pseudo-shifts on spaces of vanishing sequences. Frequently hypercyclic translation semigroups on weighted -spaces are also characterized.
During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss...
We introduce several notions of linear dynamics for multivalued linear operators (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos. We also consider the case of disjointness, in which any of these properties are simultaneously satisfied by several operators. We revisit some sufficient well-known computable criteria for determining those properties. The analysis of the dynamics of extensions of linear operators...
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