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In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The author does not give any proof, it is just a remark.

Does anyone have a reference for the proof of this fact?

Thank you !

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    $\begingroup$ The Taylor expansion of the center manifold is unique to any order. That makes the center manifold unique in the class of analytic manifolds, if an analytic center manifold exists. $\endgroup$
    – Michael Renardy
    Commented Feb 18, 2015 at 15:08

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