Chaotic behaviour on invariant sets of linear operators

Abstract

We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to establish links between the fact of satisfying any of these properties on certain invariant sets, and the analogous property on the closed span of the invariant set. We also give examples that illustrate these results.

The measure-theoretic part of the paper is now a new article entitled "Strong mixing measures for linear operators and frequent hypercyclicity". The topological part is being completed with further results

References in corpus (3)

• Strong mixing measures for linear operators and frequent hypercyclicity
• Hypercyclic operators on topological vector spaces
• Strong mixing measures for $C_0$-semigroups

Cited by in corpus (1)

• Dynamics of shift operators on non-metrizable sequence spaces