Invertible Contractions and Asymptotically Stable ODE’S that are not C1-Linearizable

Abstract

We present an example of a contraction diffeomorphism in infinite dimensions that is not C1-linearizable, and we construct a regular ordinary differential equation in a Hilbert space whose time-one map is that diffeomorphism. With this we have an example of an asymptotically stable ODE that is not C1-conjugate to its linear part.