  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 $d\leq 4$. 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 $\R^{3}$ of the linearizability criteria
in $\R^2$.

Classical Analysis and ODEs