“…In [Pilyugin, 1999], the authors proved that if a closed invariant set is hyperbolic for a diffeomorphism then the diffeomorphism has the limit shadowing property (see [Pilyugin, 1999, Theorem 1.41]). Recently, Lee [2012] showed that C 1 -generically, if a diffeomorphism has the limit shadowing property on the locally maximal homoclinic class, then it is hyperbolic. Finally, the weak limit shadowing property was introduced and studied in [Lee, 2001].…”