Oriented and standard shadowing properties for topological flows

Sogo Murakami

Published 2022-05-18Version 1

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 $\phi_1 \times \phi_2$ of two topological flows has the oriented shdowing property if $\phi_1$ with finite singuralities has the oriented shadowing property, while $\phi_2$ has the limit set consisting of finite singularities that are Lyapunov stable or Lyapunov unstable.