Showing math.DSShow all
2 papers · 1 filter
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
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…