"Smooth conjugacy of center manifolds", Proc. R. S. Edinburgh (Sect. A) 120 (1992), pp. 61-77
Center manifolds are routinely used to reduce the number of degrees of freedom in bifurcation problems. It is a well known fact, that, unfortunately, local center manifolds are typically not unique.

We show that any two local center manifolds cannot differ too much. Indeed, using foliations induced by the flow, we construct between any two such manifolds a diffeomorphism which respects the flow. Our results apply to ordinary differential equations, as well as to infinite-dimensional dynamical systems generated by certain classes of partial differential equations.

KEY WORDS: stable/unstable manifolds, stable/unstable invariant foliations, inertial manifolds, smooth cut-off, analytical/strongly continuous semigroup

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