4 citations · 14 across the 15 of their papers we have counts for
Showing 2018Show all
3 papers · 1 filter
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
Self-similarity of bubbles
Nataliya Goncharuk
Bubbles is a fractal-like set related to a circle diffeomorphism; they are a complex analogue to Arnold tongues. In this article, we prove an approximate self-similarity of bubbles…
math.DS2018★ 4 cited
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,…