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Orbital shadowing for \(C^1\)-generic volume-preserving diffeomorphisms. (English) Zbl 1470.37033

Summary: We show that \(C^1\)-generically, if a volume-preserving diffeomorphism has the orbital shadowing property, then the diffeomorphism is Anosov.

MSC:

37C20 Generic properties, structural stability of dynamical systems
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
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