Approximation scheme of a center manifold for functional differential equations (Q1378716)

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.