LAUSR

Shadowing property and structural stability are important dynamics with close relationship. Pilyugin and Tikhomirov proved that Lipschitz shadowing property implies the structural stability[ 5 ]. Todorov gave a similar result that Lipschitz two-sided limit shadowing property also implies structural stability for diffeomorpshisms[ 10 ]. In this paper, we define a generalized Lipschitz shadowing property which unifies these two kinds of Lipschitz shadowing properties, and prove that if a diffeomorphism \begin{document}$ f $\end{document} of a compact smooth manifold \begin{document}$ M $\end{document} has this generalized Lipschitz shadowing property then it is structurally stable. The only if part is also considered.