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The Two-Fixed Point Lemma


  • Oleg Kozlovski
  • Sebastien van Strien
  • Robin de Vilder


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.

Suggested Citation

  • Oleg Kozlovski & Sebastien van Strien & Robin de Vilder, 2001. "The Two-Fixed Point Lemma," DELTA Working Papers 2001-01, DELTA (Ecole normale supérieure).
  • Handle: RePEc:del:abcdef:2001-01

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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