97-518 Rayskin V.

$\alpha $-H\"{o}lder linearization (29K, LaTeX) Sep 23, 97

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Abstract. A well known theorem of Hartman-Grobman says that a $C^2$ diffeomorphism $f : \bf R^n \rightarrow \bf R^n $ with a hyperbolic fixed point at $0$ can be topologically conjugated to the linear diffeomorphism $L = df(0)$ (in a neighborhood of $0$). On the other hand, if a non-planar map has resonance, then linearization may not be $C^1$. A counter-example is due to P. Hartman (see \cite{H2}). In this paper we will show that for any $\alpha \in (0,1)$ there exists an $\alpha $-H\"{o}lder linearization in a neighborhood of $0$ for the counter-example of Hartman. No resonance condition will be required. A linearization of a more general map will be discussed.

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