Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing

Pilyugin, Sergei Yu.; Sakai, Kazuhiro; Tarakanov, O. A.

doi:10.3934/dcds.2006.16.871

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Cited by 12 publications

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“…The weak shadowing property was introduced in [11]. The weak shadowing property is investigated in [10,11,12,13,14]. Every diffeomorphism having the shadowing property has the weak shadowing property but the converse is not true.…”

Section: Introductionmentioning

confidence: 99%

Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing

Lee¹

2011

Preprint

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Let f be a volume-preserving diffeomorphism of a closed C ∞ two-dimensional Riemannian manifold M. In this paper, we prove the equivalence between the following conditions:(a) f belongs to the C 1 -interior of the set of volume-preserving diffeomorphisms which satisfy the weak shadowing property. (b) f belongs to the C 1 -interior of the set of volume-preserving diffeomorphisms which satisfy the limit weak shadowing property, (c) f is Anosov.

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Section: Introductionmentioning

confidence: 99%