Abstract
Let f be a diffeomorphism of a closed manifold M, and let be a closed f-invariant set. In this paper, by applying the reasoning developed in Wen et al. [J. Differ. Equ. 246 (2009), pp. 340–357] based on Liao, we study chain transitive sets in view of shadowing theory, and it is proved that is chain transitive and -stably shadowing if and only if is hyperbolic basic set. As a corollary, for a chain component of f, it is proved that is -stably shadowing if and only if is a hyperbolic homoclinic class.
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