Bifurcations of the ‘heart’ polycycle in generic 2-parameter families

Dukov, A.

doi:10.1090/mosc/284

Bifurcations of the ‘heart’ polycycle in generic 2-parameter families
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by A. V. Dukov
Translated by: Ian Marshall

Trans. Moscow Math. Soc. 2018, 209-229

DOI: https://doi.org/10.1090/mosc/284

Published electronically: November 29, 2018

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Abstract:

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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