A Partial Reciprocal of Dirichlet Lagrange Theorem Detected by Jets

作者：de Pera Garcia Manuel Valentim; Alva Morales Gerard John

来源：Qualitative Theory of Dynamical Systems, 2017, 16(2): 371-389.

DOI：10.1007/s12346-016-0196-x

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.

• 出版日期2017-7