Linearizations of ordinary differential equations by area preserving maps

Source abstract

We clarify the class of second and third order ordinary differential equations which can be tranformed to the simplest equations Y ″ = 0 and Y ‴ = 0. The coordinate changes employed to transform the equations are respectively area preserving maps for second order equations and contact form preserving maps for third order equations. A geometric explanation of the results is also given by using connections and associated covariant differentials both on tangent and cotangent spaces.