Foliations consistent with systems of differential equations of arbitrary-order (Q1333632)

The author considers foliations consistent with some systems of ordinary differential equations and shows that they are consistent also with systems of paths built from solutions of ordinary differential equations. Therefore, the results of the author's earlier paper [Sov. Math. 33, No. 7, 5-15 (1989); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1989, No. 7(326), 5-13 (1989; Zbl 0683.53032)], remain valid for foliations considered here. The paper is dotted with misprints and other mistakes changing its mathematical meaning. For example, conditions P1--P3 imply that \(P(x)\) consists of all the piecewise smooth curves on \(X\) originated at \(x\). This makes all the consideration meaningless. Also, the language of the English translation is a bit strange.