Abstract
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.
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