A. V. Osipov
Russia, 195197, Saint-Petersburg, Metallistov pr., 118,
St. Petersburg State University,
Faculty of Mathematics and Mecanics,
We study the first and second weak limit shadowing properties of nonlinear dynamical systems and their "negative" analogs. It is shown that any dynamical system with compact phase space has the second weak limit shadowing property. We give an example of a two-dimensional sphere diffeomorphism that has the first weak limit shadowing property, but does not have its "negative" analog. It is proved that the C1-interior of the set of diffeomorphisms of a two-dimensional smooth closed manifold having the first weak limit shadowing property coincides with the set of Ω-stable diffeomorphisms.