Orbital and weak shadowing properties (Q1865957)

The authors consider three generalizations of the classical shadowing property. They show that for linear automorphisms of \(\mathbb{C}^n\) two of them coincide with the classical one. Then, they show that on a compact manifold the \(C^1\) interior of the set of diffeomorphisms satisfying the orbital shadowing property coincides with the set of structurally stable diffeomorphisms.