Hyperbolic manifolds with the strongly shadowing property

Publisher： Cambridge University Press

E-ISSN： 1755-1633|60|1|37-43

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.60, Iss.1, 1999-08, pp. : 37-43

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Abstract

Let f be a C1 diffeomorphism of a compact smooth manifold M and λ ⊂ M a C1 compact invariant submanifold with a hyperbolic structure as a subset of M. We show that the diffeomorphism | λ is Anosov if and only if λ has the strongly shadowing property, and find hyperbolic sets which have the strongly shadowing property.

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