Limit Inverse Shadowing Property And Strong Inverse Shadowing Property Of A Diffeomorphism F In Dynamical Systems

Content: The shadowing property was advanced by D. V. Anosov in1976 when he discussed the qeodesic manifold in differentiable mani-fold with the negative curvature. It plays an important role not only instability theory of dynamical systems, but also in calculate maths. Pi-lyugin and Corless introduced the definition of the inverse shadowingproperty and obtained some important results.In this paper, we study the limit inverse shadowing property andthe strong inverse shadowing property of a diffeomorphism f in thehyperbolic invariant sets.On the basis of the limit shadowing property, the strong shadow-ing property and the inverse shadowing property, we define the limitinverse shadowing property and the strong inverse shadowing prop-erty in the discrete dynamical system. Let f be a diffeomorphism.It is shown that (â…°) f has the limit inverse shadowing property andthe strong inverse shadowing property on the hyperbolic invariant set;(â…±) an expansive diffeomorphism f has the strong inverse shadowingproperty if f has the strong shadowing property.