Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.
@article{urn:eudml:doc:38481, title = {Linearisation of second-order differential equations.}, journal = {Extracta Mathematicae}, volume = {11}, year = {1996}, pages = {155-162}, mrnumber = {MR1424752}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38481} }
Martínez, Eduardo. Linearisation of second-order differential equations.. Extracta Mathematicae, Tome 11 (1996) pp. 155-162. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38481/