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I have a Hamiltonian system and I have to classify its equilibrium points according to Lyapunov-stability. For me it is quite clear that minimum points of potential energy are points of stable equilibrium. However, I could not prove that the other points are unstable. I suppose this can be proved via a Chetaev function, but I did not get a good choice for that function. I'm using the definitions and theorems of that reference: http://www.scholarpedia.org/article/Chetaev_function

Anyone have any hint on how to prove this result?

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