Bagderina, Yulia Yu Linearization criteria for a system of two second-order ordinary differential equations. (English) Zbl 1213.34056 J. Phys. A, Math. Theor. 43, No. 46, Article ID 465201, 34 p. (2010). For a system of second-order ordinary differential equations \[ x''=f(t,x,x'),\quad x\in\mathbb R^n, \]conditions of its linearizability to the form \(z''=0\), \(z\in\mathbb R^n\), are well known. However, an arbitrary linear system needs not to be equivalent via an invertible point transformation to this simplest form. The paper provides criteria for a system of two second-order equations to be mapped to a linear system of general form. Necessary and sufficient conditions for linearization by means of a point transformation are given in terms of the system coefficients. The results obtained are illustrated by examples. Reviewer: Eugene Ershov (St. Petersburg) Cited in 14 Documents MSC: 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms Keywords:systems of second-order ordinary differential equations; linearization problem PDFBibTeX XMLCite \textit{Y. Y. Bagderina}, J. Phys. A, Math. Theor. 43, No. 46, Article ID 465201, 34 p. (2010; Zbl 1213.34056) Full Text: DOI