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Linear chaos on Fréchet spaces. (English) Zbl 1079.47008
A complete, metrizable, locally convex space over the real or complex numbers is called a Fréchet space. A continuous linear operator \(T: E \rightarrow E\) from a Fréchet space \(E\) into itself is called hypercyclic if there exists an \(x \in E\) such that its orbit \(\text{Orb}(T,x)\) by \(T\) is dense in \(E\).
In this paper, the authors review some recent results on hypercyclicity and chaos of continuous linear operators between Fréchet spaces.

MSC:
47A16 Cyclic vectors, hypercyclic and chaotic operators
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
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