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math.DS2026
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…
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…