$C^1$-stably shadowable conservative diffeomorphisms are Anosov

M\'{a}rio Bessa

doi:10.4134/BKMS.2013.50.5.1495

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Bull. Korean Math. Soc. 2013; 50(5): 1495-1499

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1495

$C^1$-stably shadowable conservative diffeomorphisms are Anosov

M\'{a}rio Bessa

Universidade da Beira Interior

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Abstract

In this short note we prove that if a symplectomorphism $f$ is $C^1$-stably shadowable, then $f$ is Anosov. The same result is obtained for volume-preserving diffeomorphisms.

Keywords: Anosov maps, shadowing, uniform hyperbolicity

MSC numbers: 37D20, 37C50

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$C^1$-stably shadowable conservative diffeomorphisms are Anosov

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$C^1$-stably shadowable conservative diffeomorphisms are Anosov

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Article Tools

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Share this article on :

Related articles in BKMS

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Bulletin of the
Korean Mathematical Society BKMS