Singular PDEs and the problem of finding invariant manifolds for nonlineardynamical systems

The present research work proposes a new approach to the problem of finding invariant manifolds for nonlinear real analytic dynamical systems. The for mulation of the problem is conveniently realized through a system of singul ar first-order quasi-linear partial differential equations (PDEs) and a rat her general set of conditions for solvability is derived using Lyapunov's a uxiliary theorem. The solution of the aforementioned system of PDEs is prov en to be a locally analytic invariant manifold that under certain condition s coincides with the stable or unstable manifold, and which can he easily c omputed with the aid of a symbolic software package. (C) 2000 Elsevier Scie nce B.V. All rights reserved.