Asymptotic expansions of invariant manifolds. II (Q920266)

[For part I see ibid. 39, No.4, 411-418 (1987; Zbl 0657.34055).] For a system of the form \[ d\Theta /dt=w+F(\Theta,x,y,\epsilon),\quad dx/dt=Ax+H(\Theta,x,y,\epsilon),\quad dy/dt=By+G(\Theta,x,y,\epsilon), \] the existence of an approximate invariant manifold given by \(y=\phi (\Theta,x)+\sum^{k}_{i=0}\epsilon^{i+1} \phi_ i(\Theta,x)\) is proved where the precision belongs to the interval (0,\(\epsilon\) b). The value of b is described in terms of the entries of the equations.