Flows with the weak two-sided limit shadowing property

In this paper we study the weak two-sided limit shadowing for flows on a compact metric space which is different with the usual shadowing, two-sided limit shadowing and L-shadowing, and characterize the weak two-sided limit shadowing flows from the pointwise and measurable viewpoints. Moreover, we prove that if a flow \begin{document}$ \phi $\end{document} has the weak two-sided limit shadowing property on its chain recurrent \begin{document}$ CR(\phi) $\end{document} then the set \begin{document}$ CR(\phi) $\end{document} is decomposed by a finite number of closed invariant sets on which \begin{document}$ \phi $\end{document} is topologically transitive and has the two-sided limit shadowing property.