Geodesic
Small Amplitude Limit Cycles for Cubic Systems
Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 54-63

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DOI

In this article we study the simultaneous generation of limit cycles out of singular points and infinity for the family of cubic planar systems With a suitable choice of parameters, the origin and four other singularities are foci and infinity is a periodic orbit. We prove that it is possible to obtain the following configuration of limit cycles: two small amplitude limit cycles out of the origin, a small amplitude limit cycle out of each of the other four foci, and a large amplitude limit cycle out of infinity. We also obtain other configurations with fewer limit cycles.
DOI : 10.4153/CMB-1993-009-4
Mots-clés : 58F21, 34C05 
Guíñez, V.; Sáez, E.; Szántó, I. Small Amplitude Limit Cycles for Cubic Systems. Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 54-63. doi: 10.4153/CMB-1993-009-4
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     author = {Gu{\'\i}\~nez, V. and S\'aez, E. and Sz\'ant\'o, I.},
     title = {Small {Amplitude} {Limit} {Cycles} for {Cubic} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {54--63},
     year = {1993},
     volume = {36},
     number = {1},
     doi = {10.4153/CMB-1993-009-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-009-4/}
}
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