Dynamical Systems Without Closed Integral Curves

  • Diethard Pallaschke
Conference paper


Starting point of this paper is an article of Medvedev [1970]. In this article Medvedev states sufficient conditions for a dynamical system on an n-dimensional simply connected manifold to have no closed integral curves. The special case n = 2 has been treated by Poincare/Bendixson (see [1955]), the case n = 3 has been studied by Demidowitsch [1966]. For applications to economics we refer to the paper of Rose [1967], where this theory is used for the study of the employment cycle.


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  1. Demidowitsch, W.B.: Eine Verallgemeinerung des Kriteriums von Bendixson. ZAMM 46, 1966, 145–146.CrossRefGoogle Scholar
  2. Medvedev, V.S.: Sufficient Conditions for Dynamical Systems to Have no Integral Cycles. Differentsial’nye Uravneniya 6, 1970, 454–466.Google Scholar
  3. Poincare, A., and J. Bendixson: Theory of Ordinary Differential Equations. E.A. Coddington and N. Levinson. Chapter 16, 389–403. New York 1955.Google Scholar
  4. Rose, H.: On the Non-Linear Theory of the Employment Cycle. Review of Economic Studies 34, 1967, 153–173.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1983

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  • Diethard Pallaschke

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