Relations between Shadowing and Inverse Shadowing in Dynamical Systems

In this paper, we study relations between shadowing and inverse shadowing for homeomorphisms of a compact space. We present an example of a smooth diffeomorphism of a compact three-dimensional manifold that has the shadowing property and does not have the inverse shadowing property. For some classes of inverse shadowing, we construct examples of homeomorphisms that have the inverse shadowing property but do not have the shadowing property.

Some General Properties of the Inverse Shadowing Property

The inverse shadowing property is concentrated, it has important properties and applications in maths. In this paper, some general properties of this concept are proved. Let ( be a metric space: ( → ( be maps have the inverse shadowing property. We show the maps ∘ , have the inverse shadowing property. If and :( , ????) →( ,????) are mapped on a metric space ( ,????) have the inverse shadowing property, We show the maps + and . have the inverse shadowing property.