Abstract
We study the normalization obtained by C. Foias and J. C. Saut for the Navier–Stokes equations in the classical case of analytic ordinary differential equations in the neighborhood of a stationary point. We show that in this general (finite-dimensional) case, this normalization coincides with the distinguished normalization in the sense of A. D. Brjuno. Moreover, their approach leads to a spectral formula for the (inverse of the) distinguished normalizing map. In the particular case of an asymptotically stable, by linearization, stationary point, the Foias–Saut device gives the inverse of the already known link between the Lyapunov exponential expansion and normalization.
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