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Germs of bifurcation diagrams and SN–SN familiesстатья
- Автор: Ilyashenko Yu
- Журнал: Chaos: An Interdisciplinary Journal of Nonlinear Science
- Том: 31
- Номер: 1
- Год издания: 2021
- Первая страница: 013103
- DOI: 10.1063/5.0030742
- Аннотация: We study the geometry of the bifurcation diagrams of the families of vector fields in the plane. Countable number of pairwise non-equivalent germs of bifur-cation diagrams in the two parameter families is constructed. Before this effect was discovered for three parameters only. Our example is related with so called SN - SN families: unfoldings of vector fields with one saddle-node singular point and one saddle-node cycle. We prove structural stability of this family. By the way, the tools that may be helpful in the proof of structural stability of other generic two-parameter families are developed. One of these tools is the embedding theorem for saddle-node families depending on the parameter. It is proved at the end of the paper.
- Добавил в систему: Ильяшенко Юлий Сергеевич