# American Institute of Mathematical Sciences

June  2009, 24(2): 315-329. doi: 10.3934/dcds.2009.24.315

## Hölder stability of diffeomorphisms

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

Received  June 2008 Revised  November 2008 Published  March 2009

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.
Citation: Jinpeng An. Hölder stability of diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 315-329. doi: 10.3934/dcds.2009.24.315
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