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• W2963782565 endingPage "2982" @default.
• W2963782565 startingPage "2963" @default.
• W2963782565 abstract "We study various types of shadowing properties and theirimplication for $C^1$ generic vector fields. We show that,generically, any of the following three hypotheses implies that anisolated set is topologically transitive and hyperbolic: (i) theset is chain transitive and satisfies the (classical) shadowingproperty, (ii) the set satisfies the limit shadowing property, or(iii) the set satisfies the (asymptotic) shadowing property withthe additional hypothesis that stable and unstable manifolds ofany pair of critical orbits intersect each other. In our proof weessentially rely on the property of chain transitivity and, inparticular, show that it is implied by the limit shadowingproperty. We also apply our results to divergence-free vectorfields." @default.
• W2963782565 created "2019-07-30" @default.
• W2963782565 creator A5026609529 @default.
• W2963782565 date "2014-01-01" @default.
• W2963782565 modified "2023-09-25" @default.
• W2963782565 title "Hyperbolicity and types of shadowing for $C^1$ generic vector fields" @default.
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• W2963782565 doi "https://doi.org/10.3934/dcds.2014.34.2963" @default.
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