A numerical procedure is described that can accurately compute the stable manifold of a saddle fixed point for a map of ℝ2, even if the map has no inverse. (Conventional algorithms use the inverse map to compute an approximation of the unstable manifold of the fixed point.) We rigorously analyze the errors that arise in the computation and guarantee that they are small. We also argue that a simpler, nonrigorous algorithm nevertheless produces highly accurate representations of the stable manifold.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics