Stably usual limit shadowing property and partially hyperbolic (Q2837889)
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scientific article; zbMATH DE number 6184884
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stably usual limit shadowing property and partially hyperbolic |
scientific article; zbMATH DE number 6184884 |
Statements
8 July 2013
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limit shadowing property
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homoclinic classes
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dominated splittings
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partially hyperbolic
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Stably usual limit shadowing property and partially hyperbolic (English)
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Let \(M\) be a closed \(C^\infty\) manifold, and \(f\) a diffeomorphism of \(M\). Let \(p\) be a hyperbolic periodic point of \(f\), and \(H_f(p)\) the homoclinic class of \(p\). In this paper, the author proves that if \(f\) has the \(C^1\)-stably usual limit shadowing property on \(H_f(p)\), then \(H_f(p)\) admits a dominated splitting. Moreover, if in addition \(M\) is three-dimensional, then \(H_f(p)\) is partially hyperbolic.
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