ИСТИНА

We study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a compact non-degenerate singular fibre satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighbourhood of such a fibre is preserved after any such perturbation. We also give a classification, up to real-analytic symplectic equivalence, of the Lagrangian fibrations in a neighbourhood of such a fibre.