Dynamical Systems Without Closed Integral Curves
Starting point of this paper is an article of Medvedev . 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 ), the case n = 3 has been studied by Demidowitsch . For applications to economics we refer to the paper of Rose , where this theory is used for the study of the employment cycle.
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- Medvedev, V.S.: Sufficient Conditions for Dynamical Systems to Have no Integral Cycles. Differentsial’nye Uravneniya 6, 1970, 454–466.Google Scholar
- 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