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.

Weak instability of Hamiltonian equilibria.

ZAMPIERI, Gaetano
2012

Abstract

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.
Hamiltonian systems; Lyapunov stability; Asymptotic motions
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/619356
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