Singular PDEs and the problem of finding invariant manifolds for nonlinear dynamical systems

摘要

The present research work proposes a new approach to the problem of finding invariant manifolds for nonlinear real analytic dynamical systems. The formulation of the problem is conveniently realized through a system of singular first-order quasi-linear partial differential equations (PDEs) and a rather general set of conditions for solvability is derived using Lyapunov's auxiliary theorem. The solution of the aforementioned system of PDEs is proven to be a locally analytic invariant manifold that under certain conditions coincides with the stable or unstable manifold, and which can he easily computed with the aid of a symbolic software package. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 18]