On the Lagrange-Dirichlet converse in dimension three

2022/08/01 by Burgos, Juan M., Paternain, Miguel
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.01139

Abstract

Consider a mechanical system with a real analytic potential. We prove that in dimension three, there is an open and dense subset of the set of non strict local minimums of the potential such that every one of its points is a Lyapunov unstable equilibrium point.

Related

• A proof of the Palamodov's total instability conjecture
• On the Lyapunov instability in Newtonian dynamics
• Lyapunov unstable elliptic equilibria
• A partial reciprocal of Dirichlet Lagrange Theorem detected by Jets
• Discrete conditions of Lyapunov stability