Totally ergodic shadowing property on noncompact metric spaces

Abstract

In this paper, we study the ergodic shadowing property for dynamical systems on noncompact metric spaces. More precisely, under the condition of bi-uniform continuity of homeomorphisms on a metric space, we show that a homeomorphism on a metric space has the ergodic shadowing property if and only if it has the totally ergodic shadowing property. We also investigate some recurrences and dynamical properties of the ergodic shadowing property. Furthermore, we give some examples related to our results.