Hölder stability of diffeomorphisms

Jinpeng An

doi:10.3934/dcds.2009.24.315

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2009, Volume 24, Issue 2: 315-329. Doi: 10.3934/dcds.2009.24.315

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Hölder stability of diffeomorphisms

Jinpeng An^1,

1.
School of Mathematical Sciences, Peking University, Beijing, 100871

Received: May 31, 2008

Revised: October 31, 2008

Published: May 2009

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Abstract

We prove that a $C^2$ diffeomorphism $f$ of a compact manifold $M$ satisfies Axiom A and the strong transversality condition if and only if it is Hölder stable, that is, any $C^1$ diffeomorphism $g$ of $M$ sufficiently $C^1$ close to $f$ is conjugate to $f$ by a homeomorphism which is Hölder on the whole manifold.

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Mathematics Subject Classification: Primary: 37C75, 37D20.

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