4 papers · 1 filter
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…
New Numerical Invariants of an Unfolding of a Polycycle "Tears of the Heart"
Yulij Ilyashenko, Stanislav Minkov, Ivan Shilin
In this paper new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connectio…
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…
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…