Abstract
We show that if a Hamiltonian system has the robustly orbitally shadowing property, then it is Anosov. Moreover, if a Hamiltonian system has the robustly orbitally inverse shadowing property with respect to the class of continuous methods, then it is Anosov.
Highlights
The various shadowing theory is close to the stability theory
Pilyugin et al [ ] proved that if a diffeomorphism belongs to the set of all diffeomorphisms having the orbital shadowing property, it is a structurally stable diffeomorphism
The notion of the inverse shadowing property is a dual notion of the shadowing property which was introduced by Corless and Pilyugin in [ ]
Summary
The various shadowing theory (shadowing, orbital shadowing, inverse shadowing, orbital inverse shadowing property) is close to the stability theory. It was proved in [ ] that if a diffeomorphism belongs to the C -interior of the set of all diffeomorphisms having the orbital inverse shadowing property with respect to the continuous methods, it is a structurally stable diffeomorphism.
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