4 citations · 7 across the 8 of their papers we have counts for
9 papers
Circle homeomorphisms with breaks with no conjugacy
Nataliya Goncharuk, Konstantin Khanin, Yury Kudryashov
The rigidity theory for circle homeomophisms with breaks was studied intensively in the last 20 years. It was proved that under mild conditions of the Diophantine type on the rotat…
Families of vector fields with many numerical invariants
Nataliya Goncharuk, Yury Kudryashov
We study bifurcations in finite-parameter families of vector fields on . Recent papers by Yu. Ilyashenko, N. Goncharuk, Yu. Kudryashov, I. Schurov, and N. Solodovnikov provide…
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…
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…
Spectra of quadratic vector fields on : The missing relation
Yury Kudryashov, Valente Ramírez
Consider a quadratic vector field on having an invariant line at infinity and isolated singularities only. We define the extended spectra of singularities to be the…
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…
Bounded limit cycles of polynomial foliations of
Nataliya Goncharuk, Yury Kudryashov
In this article we prove in a new way that a generic polynomial vector field in possesses countably many homologically independent limit cycles. The new proof needs n…
Genera of non-algebraic leaves of polynomial foliations of
Nataliya Goncharuk, Yury Kudryashov
In this article, we prove two results. First, we construct a dense subset in the space of polynomial foliations of degree such that each foliation from this subset has a leaf w…
Bony attractors in higher dimension
Yury Kudryashov
In this article, we extend the phenomena of a bony attractor from a rather artificial class of step skew products to the class of diffeomorphisms on the Cartesian product of the tw…