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Topology of typical corank-1 singularities for integrable systems with 3 degrees of freedomтезисы доклада Тезисы
- Авторы: Kibkalo V.A., Kudryavtseva E.A.
- Сборник: Third International Conference on Integrable Systems and Nonlinear Dynamics, and School "Integrable and Nonlinear Days" : Book of Abstracts. Yaroslavl: YarSU, 2021 .– 114 p. – (October 4–8, 2021, Yaroslavl)
- Тезисы
- Год издания: 2021
- Издательство: Ярославский государственный университет им. П.Г. Демидова
- Местоположение издательства: Ярославль
- Первая страница: 48
- Последняя страница: 49
- Аннотация: We study topology of typical 2-parameter bifurcations of parabolic orbits with (twisting) resonances. Such bifurcations occur for (structurally stable, degenerate) corank-1 local singularities of integrable systems with 3 degrees of freedom. When the resonance order equals 1,2,4,5 or 6, one knows an explicit formula (due to G. Wassermann, 1988) for the momentum map of the singular Lagrangian fibration in a neighbourhood of such a singularity. When the resonance order equals 4, we obtain the following results. We describe a stratification of the 2D space of small parameters, and the phase portrait of the reduced system in dependence on the stratum containing the given pair of parameter values. We describe the local bifurcation diagram and bifurcation complex at the singularity. We also describe the topology of the (nondegenerate) hyperbolic non-splitting singularities adjacent to the given (degenerate) singularity.
- Добавил в систему: Кудрявцева Елена Александровна