Geodesic
On dynamical systems close to Hamiltonian with separatrix loops of a~saddle
Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 79-91

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A system of two ordinary autonomous differential equations with a small parameter $\mu$ is considered on the two-dimensional Euclidean plane $R^2$. A condition for the birth of a limit cycle from a separatrix loop of a saddle of a Hamiltonian system is found for $\mu\ne0$. 
@article{SM_1995_83_1_a3,
     author = {V. S. Medvedev and E. L. Fedorov},
     title = {On dynamical systems close to {Hamiltonian} with separatrix loops of a~saddle},
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     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_1_a3/}
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V. S. Medvedev; E. L. Fedorov. On dynamical systems close to Hamiltonian with separatrix loops of a~saddle. Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 79-91. http://geodesic.mathdoc.fr/item/SM_1995_83_1_a3/