
Journal of Lie Theory 34 (2024), No. 1, 093112 Copyright Heldermann Verlag 2024 σSymmetries and First Integral of Differential Equations Xuefeng Zhao College of Mathematics, Jilin University, Changchun, P.R.China zhaoxf20@mails.jlu.edu.cn Yong Li College of Mathematics, Jilin University, Changchun, P.R.China liyong@jlu.edu.cn We provide some geometric properties for σsymmetries of system of ordinary differential equations. According to the corresponding geometric representation of σsymmetries and solvable structure, we give the first integrals for the system of firstorder ordinary differential equations and for the system of norder ordinary differential equations which has not enough symmetries and λsymmetries. Keywords: First integral, Frobenius integrable, sigmasymmetries. MSC: 34A26, 34A34, 34C40. [ Fulltextpdf (176 KB)] for subscribers only. 