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arXiv · 2112.00130

Structurally stable non-degenerate singularities of integrable systems

E. A. Kudryavtseva·A. A. Oshemkov
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Abstract

In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a 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. As an illustration, we show that a saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations, but structurally unstable under $C^\infty$ smooth integrable perturbations.

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E. A. Kudryavtseva, A. A. Oshemkov. 2021-11-30. Structurally stable non-degenerate singularities of integrable systems. https://doi.org/10.1134/s106192082201006x

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