Invertible contractions and asymptotically stable ODE´s that are not C<sup>1</sup>-linearizable
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We present an example of a contraction di®eomorphism in in¯nite dimensions that is not C1-linearizable, and we construct a regular ordinary di®erential equation in a Hilbert space whose time-one map is that di®eomorphism. With this we have an example of an asymptotically stable ODE that is not C1-conjugate to its linear part.