2012/10/04 by Gaetano Zampieri, Zampieri, Gaetano
Mathematics · #34D20 #37J25 #70H14 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:34D20 #msc:37J25 #msc:70H14
paper · pdf · doi:10.48550/arxiv.1210.1334
arxiv created 2012/10/04 · arxiv updated 2012/10/05
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit point as time goes to minus infinity. This is done by means of some examples. In particular, we show that a weakly unstable equilibrium point can be stable for the linearized vector field.