E. Mart'inez, J. F. Cari~nena
Geometric characterization of linearisable second order
differential equations.
(31K, LaTeX)

ABSTRACT.  Given an Ehresmann connection on the tangent bundle $\map{\tau}{TM}{M}$
we define a linear connection on the pull--back bundle $\tau^*(TM)$. 
With the aid of this tool, necessary and sufficient conditions for the
existence of local coordinates in which a system of second--order
differential equations is linear are derived.