3 papers
math.DS2019
New structurally unstable families of planar vector fields
Nataliya Goncharuk, Yury G. Kudryashov, Nikita Solodovnikov
We study global bifurcations in generic 3-parameter families of vector fields on . In the recent article [arXiv:1506.06797], Ilyashenko, Kudryashov, and Schurov show that 3-pa…
math.DS2018
Bifurcations of the polycycle "tears of the heart": multiple numerical invariants
Nataliya Goncharuk, Yury Kudryashov
"Tears of the heart" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields. In [arXiv:1…
math.DS2018
Large bifurcation supports
Nataliya Goncharuk, Yulij Ilyashenko
In the study of global bifurcations of vector fields on , it is important to distinguish a set "where the bifurcation actually occurs", -- the bifurcation support. Hopefully,…