Oriented and standard shadowing properties for topological flows

Abstract

We prove that oriented and standard shadowing properties are equivalent for topological flows with finite singularites that are Lyapunov stable or Lyapunov unstable. Moreover, we prove that the direct product ${\varphi }_1\times {\varphi }_2$ of two topological flows has the oriented shdowing property if ${\varphi }_1$ with finite singuralities has the oriented shadowing property, while ${\varphi }_2$ has the limit set consisting of finite singularities that are Lyapunov stable or Lyapunov unstable.

arXiv commentSome typos are corrected. This paper will be published in Tokyo Journal of Mathematics