Stably limit weak shadowing property and partially hyperbolic (Q2837866)
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scientific article; zbMATH DE number 6184869
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stably limit weak shadowing property and partially hyperbolic |
scientific article; zbMATH DE number 6184869 |
Statements
8 July 2013
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limit weak shadowing
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dominated splittings
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homoclinic classes
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partially hyperbolic
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Stably limit weak shadowing property and partially hyperbolic (English)
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Let \(M\) be a \(C^\infty\) manifold. The author shows that if a diffeomorphism of \(M\) has the \(C^1\)-stable limit weak shadowing property on the homoclinic class of a hyperbolic periodic point, then this homoclinic class admits a dominated splitting. Moreover, under the same assumption, if, in addition, \(M\) is three-dimensional, then the homoclinic class is partially hyperbolic.
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