It is proved that if f is expanding and has the pseudo-orbit tracing property, then it has the limit shadowing property.

Some properties of the pseudo-orbit tracing property is generalized to the weak shadowing property.

The pseudo-orbit tracing property(POTP) and the average-shadowing property(ASP)were generated along with the study and development of the stability in dynamical system,and had been one of the important properties.

In this paper,we investigate shadowing property,exp-shadowing property, consistency exp-shadowing property and their relation ship for continuous maps on a compact metric space and that for the shift maps on the orbit space.

The Research on the Average Shadowing Property and the Limit Weak Inverse Shadowing Property in Discrete Dynamical Systems;

If f is homeomophism,then f has sequence pseudoorbit tracing property if and only if the shift map σ f on the limit space has sequence pseudoorbit tracing property.

In this paper,we mainly discuss the pointwise pseudo-orbit tracing property of the induced map f_∞ on the inverse limit space X_∞.

In this paper we gave a character of structurally stable diffeomorphisms via the notion of inverse shadowing and proved that a structurally stable diffeomorphism has the strong inverse shadowing property with respect to two classes of continuous methods.