Symmetries of a center singularity of a plane vector fields
Let D² ⊂ R² be a closed unit 2-disk centered at the origin O ∈ R², and F be a smooth vector field such that O is a unique singular point of F and all other orbits of F are simple closed curves wrapping once around O. Thus topologically O is a „center” singularity. Let D⁺(F) be the group of all diffe...
Збережено в:
| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/178419 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Symmetries of a center singularity of a plane vector fields / S.I. Maksymenko // Нелінійні коливання. — 2009. — Т. 12, № 4. — С. 507-526. — Бібліогр.: 18 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Let D² ⊂ R² be a closed unit 2-disk centered at the origin O ∈ R², and F be a smooth vector field such that O is a unique singular point of F and all other orbits of F are simple closed curves wrapping once around O. Thus topologically O is a „center” singularity. Let D⁺(F) be the group of all diffeomorphisms of D² which preserve orientation and orbits of F. Recently the author described the homotopy type of D⁺(F) under the assumption that the 1-jet j¹ F(O) of F at O is non-degenerate. In this paper degenerate case j¹ F(O) is considered. Under additional ” nondegeneracy assumptions” on F the path components of D⁺(F) with respect to distinct weak topologies are described. These conditions imply that for each h ∈ D⁺(F) its path component in D⁺(F) is uniquely determined by the 1-jet of h at O. |
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