Geodesic
Bifurcations of the `heart' polycycle in generic 2-parameter families
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 2, pp. 247-269.

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The paper concerns the ‘heart’ polycycle. We show that the set of vector fields containing a ‘heart’ polycycle form a Banach submanifold of codimension two in the space of smooth vector fields on a two-dimensional sphere. The bifurcation diagram of a generic family containing such a polycycle is constructed and surgery on the phase portrait is described. 
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     title = {Bifurcations of the `heart' polycycle in generic 2-parameter families},
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A. V. Dukov. Bifurcations of the `heart' polycycle in generic 2-parameter families. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 2, pp. 247-269. http://geodesic.mathdoc.fr/item/MMO_2018_79_2_a4/

[1] Ilyashenko Yu. S., Li Veigu, Nelokalnye bifurkatsii, Elektronnoe izdanie, MTsNMO, M., 2016, 327–335

[2] Malta I. P., Palis J., “Families of vector fields with finite modulus of stability”, Lecture Notes in Math., 898, Springer, Berlin–New York, 1981, 212–229 | DOI | MR | Zbl

[3] Sotomayor J., “Generic one-parameter families of vector fields on two-dimensional manifolds”, Inst. Hautes Études Sci. Publ. Math., 43 (1974), 5–46 | DOI | MR | Zbl

[4] Ilyashenko Yu., Kudryashov Yu., Schurov I., “Global bifurcations in the two-sphere: a new perspective”, Invent. Math., 213:2 (2018), 461–506 | DOI | MR | Zbl

[5] Kotova A., Stanzo V., “On few-parameter generic families of vector fields on the two-dimensional sphere”, Concerning the Hilbert 16th problem, AMS Transl. Ser. 2, 165, AMS, Providence, RI, 1995 ; Adv. Math. Sci., 23, 155–201 | MR | Zbl

[6] Andronov A. A., Pontryagin L. S., “Grubye sistemy”, DAN SSSR, 14:5 (1937), 247–250 | MR