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. 
@article{MMO_2018_79_2_a4,
     author = {A. V. Dukov},
     title = {Bifurcations of the `heart' polycycle in generic 2-parameter families},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {247--269},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2018_79_2_a4/}
}
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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/