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Distributionally \(n\)-chaotic dynamics for linear operators. (English) Zbl 1390.37066

Authors’ abstract: This paper investigates distributionally \(n\)-chaotic dynamics of linear operators on Fréchet spaces. It is shown that an uncountable distributionally scrambled sets under a linear operator may not be distributionally \(n\)-scrambled for any \(n\geq 3\). In addition, the existence of invariant distributionally \(n\)-scrambled linear manifolds for a composition operator and for a bilateral weighted shift operator are proved by explicit construction.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
47A16 Cyclic vectors, hypercyclic and chaotic operators
34C28 Complex behavior and chaotic systems of ordinary differential equations
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