On the Obstruction to Linearizability of Second-Order Ordinary Differential Equations |
| |
Authors: | V. A. Yumaguzhin |
| |
Affiliation: | 1. Program System Institute, m.Botik, Pereslavl-Zalessky, 152020, Russia. e-mail
|
| |
Abstract: | In this paper, we investigate the action of the pseudogroup of all point transformations on the bundle of equations y″=u 0(x,y)+u 1(x,y)y′+u 2(x,y)(y′)2+u 3(x,y)(y′)3. We calculate the 1st nontrivial differential invariant of this action. It is a horizontal differential 2-form with values in some algebra, it is defined on the bundle of 2-jets of sections of the bundle under consideration. We prove that this form is a unique obstruction to linearizability of these equations by point transformations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|