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math.DS2026
Diophantine "Tears of the Heart"
Yulij Ilyashenko, Stanislav Minkov, Ivan Shilin
Recent studies of topologically generic unfoldings of vector fields featuring a "tears of the heart" polycycle with one internal and one external winding separatrix have shown that…
math.DS2025
Disconnected large bifurcation supports and Cartesian products of bifurcations
Timur Bakiev, Yulij S. Ilyashenko
A bifurcation that occurs in a multiparameter family is a Cartesian product if it splits into two factors in the sense that one bifurcation takes place in one part of the phase por…
math.DS2024
Singular points in generic two-parameter families of vector fields on 2-manifold
Dmitry A. Filimonov, Yulij S. Ilyashenko
In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a la…