Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems

 Let  be a diffeomorphism map on a closed smooth manifold  for dimension   . We explain in this work any chain transitive set of generic diffeomorphism  , if a diffeomorphism  has another type of shadowing property is called, the eventual shadowing property on locally maximal chain transitive set, then  is hyperbolic. In general, the eventual fitting shadowing property is not fulfilled in hyperbolic dynamical systems (satisfy in case L is Anosov diffeomorphism map) . In this paper, several concepts were presented. These concepts can be re-examined on other important spaces, and their impact on finding dynamical characteristics that may be employed in solving some mathematical problems.