Web geometry of a system of first-order autonomous ordinary differential equations
Using Elie Cartan's method the authors consider elementary properties of a system of autonomous ordinary differential equations with respect to a pseudo-group of the so-called web transformations. Reviewer's remarks: 1) The authors use the term ``web geometry'' but it is not clear, what ``web'' they refer to. One can attach different webs to a given system of ordinary differential equations, and there is the concrete pseudo-group of admissible transformations for every type of these webs. See about them in [\textit{A. A. Duyunova}, Russ. Math. 56, No. 2, 37--49 (2012; Zbl 1257.53020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 2, 43--56 (2012); J. Math. Sci., New York 177, No. 5, 654--667 (2011; Zbl 1290.53019); translation from Fundam. Prikl. Mat. 16, No. 2, 13--31 (2010)]. 2) In Section 2 (The Cartan Equivalence Method), instead of the \(\omega^i\) symbol it is necessary to use \(\omega_i\), since it is the contravariant object. 3) On the left of equation (2.5) there has to be zero. 4) Theorems 1 and 2 are not connected to the content of the article.
autonomous ordinary differential equations
scientific article; zbMATH DE number 6494572