## 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

### Keywords:

distributional chaos; composition operator; weighted shifts
Full Text:

### References:

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