Limit sets of dynamical systems on the space of probability measures

Abstract

Let m be a dynamical system on the space of probability measures M 1( R d), and let Λ + (ϑ) be the positive limit set for ϑ ∈ M 1( R d), where ϑ has compact support K ⊂ R d . The main result of this paper states that support of Λ +(ϑ) ⊂ ▪,support of Λ + ( δ x ), where δ x is the Dirac measure at point x.