Distributionally n-chaotic dynamics for linear operators

Abstract

This paper investigates distributionally n-chaotic dynamics of linear operators on Frechet spaces. It is shown that an uncountable distributionally scrambled sets under a linear operator may not be distributionally n-scrambled for any \(n \ge 3\). 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.