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.
We give characterisations of Ω-stable diffeomorphisms and structurally stable diffeomorphisms via the notions of weak inverse shadowing and orbital inverse shadowing, respectively. More precisely, it is proved that the C1 interior of the set of diffeomorphisms with the weak inverse shadowing property coincides with the set of Ω-stable diffeomorphisms and the C1 interior of the set of diffeomorphisms with the orbital inverse shadowing property coincides with the set of structurally stable diffeomorphisms.
We discuss the relationship between ergodic shadowing property and inverse shadowing property offand that of the shift map σfon the inverse limit space.
Some General Properties of the Inverse Shadowing Property
