ABSTRACT
The Lorenz model was originally constructed by truncating Fourier expansions of the Navier–Stokes equations. The model has become some sort of a numerical laboratory because it contains in a simple manner many of the fundamental features that nonlinear models may have. In particular it has regions of turbulence or deterministic chaos. The eigenvectors of the Jacobian matrix are of course only tangent vectors to the corresponding stable or unstable manifolds. The orbit is close to the unstable manifold surface. The orbits approach the fixed point along its stable one-dimensional manifold, and indeed the orbits are identical to the stable manifolds. The orbits start out in the plane of the unstable manifolds, and must therefore continue to stay in the two-dimensional unstable manifolds.
