Introduces a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that nondegenerate critical points of the potential correspond to twist invariant tori and degenerate critical points of the potential correspond to non-twist invariant tori.
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