Shadowing and non-shadowing in dynamical systems.

This study was a survey article on shadowing property in a dynamical system given by a homeomorphism of a compact, metric space. We introduced beginners to the study of shadowing and some properties such that the cross product f × f and the composition fh had shadowing for every integer, h > 0 if f has the shadowing. And we showed the relationship with chaotic properties. We also gave an overview of the results in the topic with examples illustrating where it exists and does not exist. The self – homeomorphism map had non shadowing if it was distal on connected space or if it was on connected space with not point is minimal. Finally, every isometry of a compact Riemannian manifold of positive dimension had non shadowing. [ABSTRACT FROM AUTHOR]