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Lipeomorphisms close to an Anosov diffeomorphism

Published online by Cambridge University Press:  22 January 2016

Kentaro Takaki
Kentaro Takaki*
Affiliation:
Department of Mathematics, Nagoya University
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It is well-known that an Anosov diffeomorphism f on a compact manifold is structurally stable in the space of all C1-diffeomorphisms, with the C1-topology (Anosov [1]). In this paper we show that f is also structurally stable in the space of all lipeomorphisms, with a lipschitz topology. The proof is similar to that of the C1-case by J. Moser [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 71 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Anosov, , Geodesic flow on a Riemannian manifold with negative curvature, Trudy-Math. Just. Stekholv, Moscow, 1967.Google Scholar
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[3] Hirsch, and Pugh, , Stable manifolds and hyperbolic sets, Proc. of Symposia in Pure Math. (Global Analysis) XIX, AMS (1970), 133–163.CrossRefGoogle Scholar
[4] Moser, , On a theorem of Anosov, J. of differential equations 5 (1969), 411–440.Google Scholar
[5] Nitecki, , Differentiate dynamics, Cambridge, M.I.T. Press, 1971.Google Scholar