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• W2036096302 abstract "We study various types of shadowing properties and their implication for C1 generic vector fields. We show that, generically, any of the following three hypotheses implies that an isolated set is topologically transitive and hyperbolic: (i) the set is chain transitive and satisfies the (classical) shadowing property, (ii) the set satisfies the limit shadowing property, or (iii) the set satisfies the (asymptotic) shadowing property with the additional hypothesis that stable and unstable manifolds of any pair of critical orbits intersect each other. In our proof we essentially rely on the property of chain transitivity and, in particular, show that it is implied by the limit shadowing property. We also apply our results to divergence-free vector fields." @default.
• W2036096302 created "2016-06-24" @default.
• W2036096302 creator A5026609529 @default.
• W2036096302 date "2013-05-13" @default.
• W2036096302 modified "2023-09-27" @default.
• W2036096302 title "Hyperbolicity and Types of Shadowing for C1 Generic Vector Fields" @default.
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