Oriented and Standard Shadowing Properties for Topological Flows

Abstract

We prove that oriented and standard shadowing properties are equivalent for topological flows with finite singularities that are Lyapunov stable or backward Lyapunov stable. Moreover, we prove that the direct product $\phi_1 \times \phi_2$ of two topological flows has the oriented shadowing property if $\phi_1$ with finite singularities has the oriented shadowing property, while $\phi_2$ has the limit set consisting of finite singularities that are Lyapunov stable or backward Lyapunov stable.