The Two-Fixed Point Lemma
Complicated (chaotic), global, expectations-driven business cycles in two-dimensional models have been shown to involve non-trivial intersections of stable and unstable manifolds of a (periodic) saddle steady state. Whether similar phenomena may occur in other two-dimensional dynamic economic models in discrete time is the object of this paper. In fact, it will be shown that if the dynamics is described by an invertible map of the first orthant of the plane, the stable and unstable manifolds of a unique steady state cannot intersect non-trivially.
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