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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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    References listed on IDEAS

    1. Kiyotaki, Nobuhiro & Moore, John, 1997. "Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-248, April.
    2. Caballero, Ricardo J & Hammour, Mohamad L, 1994. "The Cleansing Effect of Recessions," American Economic Review, American Economic Association, vol. 84(5), pages 1350-1368, December.
    3. Philippe Aghion & Gilles Saint-Paul, 1998. "Uncovering Some Causal Relationships Between Productivity Growth and the Structure of Economic Fluctuations: A Tentative Survey," LABOUR, CEIS, vol. 12(2), pages 279-303, July.
    4. Klein, Benjamin & Crawford, Robert G & Alchian, Armen A, 1978. "Vertical Integration, Appropriable Rents, and the Competitive Contracting Process," Journal of Law and Economics, University of Chicago Press, vol. 21(2), pages 297-326, October.
    5. Ralph L. Nelson, 1959. "The Merger Movement from 1895 through 1920," NBER Chapters,in: Merger Movements in American Industry, 1895-1956, pages 33-70 National Bureau of Economic Research, Inc.
    6. Steven J. Davis & John Haltiwanger, 1992. "Gross Job Creation, Gross Job Destruction, and Employment Reallocation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 819-863.
    7. Devra L. Golbe & Lawrence J. White, 1988. "A Time-Series Analysis of Mergers and Acquisitions in the U.S. Economy," NBER Chapters,in: Corporate Takeovers: Causes and Consequences, pages 265-310 National Bureau of Economic Research, Inc.
    8. Ralph L. Nelson, 1959. "Merger Movements in American Industry, 1895-1956," NBER Books, National Bureau of Economic Research, Inc, number nels59-1, January.
    9. Ralph L. Nelson, 1959. "Merger Movements and Business Cycles, 1895-1956," NBER Chapters,in: Merger Movements in American Industry, 1895-1956, pages 106-126 National Bureau of Economic Research, Inc.
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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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