Separatrix and limit cycles of quadratic systems and Dulac’s theorem

Chicone, Carmen; Shafer, Douglas S.

doi:10.1090/S0002-9947-1983-0701513-X

Separatrix and limit cycles of quadratic systems and Dulac’s theorem
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by Carmen Chicone and Douglas S. Shafer PDF

Trans. Amer. Math. Soc. 278 (1983), 585-612 Request permission

Abstract:

Separatrix cycles for a planar quadratic vector field are studied. The results obtained are used to show that in any bounded region of the plane a quadratic vector field has at most a finite number of limit cycles.

References

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Mémoire sur les courbes définies par une equation différentielle

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