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Approximation scheme of a center manifold for functional differential equations. (English) Zbl 0896.34061

Consider the autonomous functional-differential equation \((*) \;dx/dt = Lx_t + f(x_t)\) where \(L\) is a bounded linear operator, \(f\) is sufficiently smooth and satisfies \(f(0)=0\), \(f'(0)=0\). Assuming that \((*)\) has a center manifold, the authors derive an algorithm to compute the terms in the Taylor expansion of this manifold up to any order.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C45 Invariant manifolds for ordinary differential equations
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