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Saddle fixed points are the centerpieces of complicated dynamics in a system.The one-dimensional stable and unstable manifolds of these saddle-points arecrucial to understanding the dynamics of such systems. While the problem ofsketching the unstable manifold is simple, plotting the stable manifold is notas easy. Several algorithms exist to compute the stable manifold ofsaddle-points, but they have their limitations, especially when the system isnot invertible. In this paper, we present a new algorithm to compute the stablemanifold of 2-dimensional systems which can also be used for non-invertiblesystems. After outlining the logic of the algorithm, we demonstrate the outputof the algorithm on several examples.

Sketching 1-D stable manifolds of 2-D maps without the inverse