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Bamòn's theorem (Theorem)

Every quadratic vector field in $ \mathbb{R}^2$ has a finite number of limit cycles.[BR]

Historical note

This theorem is weaker than Dulac's theorem but at the time of the publication of [BR] there was a problem in the proof of Dulac's theorem.

References

BR
R. Bamòn: Quadratic vector fields in the plane have a finite number of limit cycles, Publ. I.H.E.S. 64 (1986), 111-142.



"Bamòn's theorem" is owned by Daume.
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Cross-references: Dulac's theorem, limit cycles, number, finite, vector field

This is version 2 of Bamòn's theorem, born on 2004-07-14, modified 2005-02-06.
Object id is 6002, canonical name is BamonsTheorem.
Accessed 2317 times total.

Classification:
AMS MSC: 34C07 (Ordinary differential equations :: Qualitative theory :: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramif)
Pending Errata and Addenda
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