Abstract

We show how the problem of constructing an invariant manifold (of co-dimension $k$) can be locally reduced to solving a (system of $k$) quasi-linear PDE(s), which can be efficiently solved using an Ordered Upwind Method (OUM). Such methods, originally introduced in a joint work with J.A. Sethian for static Hamilton-Jacobi PDEs, rely on careful use of the direction of information propagation to systematically advance the computed "boundary" and to de-couple the discretized system. We illustrate our approach by constructing invariant manifolds of hyperbolic saddle points for several "geometrically stiff" systems. This work is a joint project with J. Guckenheimer.