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We consider the stability and instability of an equilibrium point of a Hamiltonian system of two degrees of freedom in certain resonance cases. We also consider the stability or instability of a fixed point of an area-preserving mapping in certain resonance cases. The stability criteria are established by Moser's invariant curve theorem and the instability is established by Chetaev's theorem.doi:10.1088/0951-7715/12/5/309 fatcat:lp6ala45yvgjlpxtq6j7gcv5ha