On the Compact Integral Hypersurfaces of the Multidimensional Homogeneous Darboux System

Authors: Vladimir V. Amel’kin, Valentin Yu. Tyshchenko

Keywords: system of ordinary differential equations, completely solvable system of exact differential equations, hypersurface

DOI: 10.46793/SPSUNP2401.031A

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Abstract:

The ordinary at $m=1$ and the completely solvable at $m>1$ the real homogeneous Darboux systems $$dx_i=\sum\limits_{j=1}^{m}\Bigl(L_{ij}(x)+x_iP_j(x) \Bigr)dt_j, i=\overline{1,n},$$ where $n>1,\ m