Symmetries of center singularities of plane vector fields

• Published in: Нелінійні коливання
• Date: 2010
• Main Author: Maksymenko, S.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/174925
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Symmetries of center singularities of plane vector fields / S.I. Maksymenko // Нелінійні коливання. — 2010. — Т. 13, № 2. — С. 177-205. — Бібліогр.: 30 назв. — англ.

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 θ : D² \ {O} → (0, +∞ ) be the...