C-stably Weak Shadowing Chain Components Are Partially Hyperbolic
نویسنده
چکیده
Let f be a diffeomorphism of a closed C∞ three-dimensional manifold. In this paper, we introduce the notion of C1-stably weak shadowing for a closed f -invariant set, and prove that C1-generically, for an aperiodic chain component Cf of f isolated in the chain recurrent set, if f|Cf is C 1-stably weak shadowing, then there are a C1-neighborhood U(f) of f and an open and dense subset V of U(f) such that for any g ∈ V, there is a chain component (of g nearby Cf ) which is partially hyperbolic.
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