Linearization from complex Lie point transformations

Abstract

Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\le 4$. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in ${\mathbb{R}}^3$ of the linearizability criteria in ${\mathbb{R}}^2$.

17 Pages, to appear in Journal of Applied Mathematics. arXiv admin note: substantial text overlap with arXiv:1104.3837

References in corpus (1)

• Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variables