Abstract
This paper studies the ℳ0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the ℳ0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably ℳ0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.
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