4 papers
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…
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…
Uniqueness theorem for completely non-degenerate B-groups
A. A. Glutsyuk, Yu. S. Ilyashenko
We prove that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property…
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…