4 papers
Generic families of circle diffeomorphisms have many coexisting periodic orbits
Ivan Shilin
We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which t…
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…
Sparkling saddle loops of vector fields on surfaces
Ivan Shilin
We study bifurcations of vector fields on 2-manifolds with handles in generic one-parameter families unfolding vector fields with a separatrix loop of a hyperbolic saddle. These bi…