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Euler polygons in systems with time-measurable right-hand side

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Abstract

In the present paper, we consider Euler polygons for systems with bounded time-measurable right-hand side. The convergence of Euler polygons to trajectories of the system is studied. We present counterexamples showing that the fineness of the partition does not ensure the convergence to any trajectory. Instead of fineness, we introduce a metric on the set of all possible partitions of the time interval. In terms of this metric, we indicate sufficient convergence conditions that guarantee the existence of Euler polygons that are arbitrarily close to some solutions of the system.

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Authors and Affiliations

  1. Institute for Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    D. V. Khlopin

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  1. D. V. Khlopin
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Original Russian Text © D.V. Khlopin, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1648–1657.

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Khlopin, D.V. Euler polygons in systems with time-measurable right-hand side. Diff Equat 44, 1711–1720 (2008). https://doi.org/10.1134/S0012266108120070

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  • DOI: https://doi.org/10.1134/S0012266108120070

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