InvariantManifolds.jl

The purpose of this package is to provide a convenience tool to numerically investigate the low dimensional invariant manifolds. We don't provide any numerical stability or reliable commitment.

The main idea of this package is quite simple. By using the local manifolds of saddles, extend this manifolds step by step. We just keep the points near enough to ensure the accuracy of the numerical manifolds. Usually, the curvatures of nearby points are also considered in most algorithms. We only use the distance control since the curvatures requirement often can't be satisfied after several iterations, even in most simple example.

Currently, the two-dimensional algorithm for smooth mapping is not implemented. The reasons are that I do not like the algorithms in the literatures and I can't find a neat way neither. However, I am glad if someone is interested to extend this feature to this package.