  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.
