1. Structurally stable non-degenerate singularities of integrable systems
- Author
-
Kudryavtseva, E. A. and Oshemkov, A. A.
- Subjects
Mathematics - Dynamical Systems ,Mathematics - Differential Geometry ,Mathematics - Symplectic Geometry ,37J35, 37J39, 53D20, 70E40 - 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., Comment: 25 pages, 3 figures
- Published
- 2021
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