Invariant Linearization Criteria for Systems of Cubically Nonlinear Second-Order Ordinary Differential Equations

Invariant linearization criteria for square systems of second-order quadratically nonlinear ordinary differential equations (ODEs) that can be represented as geodesic are extended to ODEs cubically in the first derivatives. It is shown there two branches problem via point transformations an arbitrary system and its reduction simplest system. One when at most cubic obtains equivalent Lie conditions such systems. We explicitly solve this branch by case a ODEs. Necessary sufficient means given terms coefficient functions A consequence our geometric approach projection ...