A type of the shadowing properties for generic view points (Q2305833)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A type of the shadowing properties for generic view points |
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A type of the shadowing properties for generic view points (English)
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20 March 2020
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Summary: We show that if a \(C^1\) generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a \(C^1\) generic vector field of a closed smooth three-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it satisfies singular Axiom A without cycles.
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average shadowing
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asymptotic average shadowing
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generic
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chain transitive
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axiom A
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singular axiom A
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Anosov
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