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

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Cited by in corpus (2)

• Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations
• Physical Significance of Noether Symmetries