We will combine the nonlinear equations with information about the local dynamics to trace out the global stable manifold of the low-inflation steady state.
This approach will allow us to compute the global stable manifold of the low-inflation steady state.
If we begin with a point on that path, very close to the low-inflation steady state, and then iterate the nonlinear system backward, we can trace out the global dynamics associated with the saddlepath--the global stable manifold.
On the other hand, the past history of the deformation is determined by the (perturbed) stable manifold.
Since the two manifolds are invariant and the Poincare map preserves orientation, the enclosed region should be mapped another enclosed region infinitely many times along the unstable manifold, as t(or z) [right arrow] [infinity], or, along the stable manifold, as t (or z] [right arrow] [infinity].