Resumen de A Partial Reciprocal of Dirichlet Lagrange Theorem Detected by Jets

Manuel Valentim de Pera Garcia, Gerard John Alva Morales

• We study the stability of an equilibrium point in a conservative Hamiltonian system in the case that equilibrium is not a minimum of the potential energy and this fact is shown by a jet of this function. Thanks to a modification of a result of Krasovskii, we prove that for a large class of systems under these conditions equilibrium is unstable and there is an asymptotic trajectory to that point.