Riemann geometry in theory of the first order systems of equations

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Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz system of equations are investigated in detail.
This report was presented at the International Conference "Differential Equations and Topology", Moskow, June 17-22, 2008

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