%0 Journal Article 
%A Murillo Arcila, Marina
%A Peris, A.
%T Chaotic Behaviour on Invariant Sets of Linear Operators
%D 2015
%U http://hdl.handle.net/10498/35530
%X We study hypercyclicity, Devaney chaos, topological mixing
properties and strong mixing in the measure-theoretic sense for opera-
tors on topological vector spaces with invariant sets. More precisely, our
purpose is to establish links between the fact of satisfying any of our
dynamical properties on certain invariant sets, and the corresponding
property on the closed linear span of the invariant set, or on the union
of the invariant sets. Viceversa, we give conditions on the operator (or
C0-semigroup) to ensure that, when restricted to the invariant set, it
satis es certain dynamical property. Particular attention is given to the
case of positive operators and semigroups on lattices, and the (invariant)
positive cone. We also present examples that illustrate these results.
%K Hypercyclic operators
%K invariant sets
%K topological mixing
%K Devaney chaos
%K mixing measures
%~ Universidad de Cádiz