4 citations · 14 across the 15 of their papers we have counts for
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math.DS2017★ 1 cited
Complex rotation numbers: bubbles and their intersections
Nataliya Goncharuk
The construction of complex rotation numbers, due to V.Arnold, gives rise to a fractal-like set "bubbles" related to a circle diffeomorphism. "Bubbles" is a complex analogue to Arn…
math.DS2017
Global bifurcations in generic one-parameter families with a parabolic cycle on
Nataliya Goncharuk, Yulij Ilyashenko, Nikita Solodovnikov
We classify global bifurcations in generic one-parameter local families of \vfs on with a parabolic cycle. The classification is quite different from the classical results pr…
math.CV2017
Cheap Complex Limit Cycles
Nataliya Goncharuk, Yury Kudryashov
Consider a holomorphic foliation with singularities of a 2-dimensional complex manifold. In this article we prove a new sufficient condition for this foliation to have countably ma…