The flow of classical mechanical cubic potential systems

Abstract

This paper describes the global flow of homogeneous polynomial potentials of degree 3 for negative and positive energy. For the negative energy case a blow up of McGehee type is enough to get the complete picture of the flow. In the positive energy case, McGehee blow up fails to give global information about the flow, but comparing with a separable case we are able to obtain all the possible asymptotic behavior of solutions, whenever the coefficients of the normal form of the potential are positive.