Chain transitivity and variations of the shadowing property

Abstract

We show that, under the assumption of chain transitivity, the shadowing property is equivalent to the thick shadowing property. We also show that, if ${\mathcal{F}}$ is a family with the Ramsey property, then an arbitrary sequence of points in a chain transitive space can be ${\it\varepsilon}$ -shadowed (for any ${\it\varepsilon}$ ) on a set in ${\mathcal{F}}$ .