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Symplectic classification of structurally stable nondegenerate semilocal singularitiesтезисы доклада Тезисы
- Автор: Kudryavtseva Elena Alexandrovna
- Сборник: Regular and Chaotic Dynamics: In memory of Alexey V. Borisov: Book of Abstracts
- Серия: ANS Conference Series
- Тезисы
- Год издания: 2021
- Место издания: Institute of Computer Science Moscow - Izhevsk
- Первая страница: 42
- Последняя страница: 44
- Аннотация: We study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a non-degenerate singular fibre satisfying the 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. We also classify Lagrangian fibrations in small neighbourhoods of such fibers up to real-analytic symplectic equivalence.
- Добавил в систему: Кудрявцева Елена Александровна