4 citations · 14 across the 15 of their papers we have counts for
19 papers
Renormalization and rigidity of analytic non-linear interval exchange transformations
Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky
We construct hyperbolic renormalization horseshoes for analytic generalized interval exchange transformations (GIETs) of bounded type and with bounded geometry, provided their boun…
Hyperbolicity of renormalization for maps with multiple breaks
Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky
We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation…
Anti-classification for flows on two-tori
Nataliya Goncharuk
We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel…
Authomorphic measures with negative exponents for multicritical circle maps
Nataliya Goncharuk, Michael Yampolsky
Authomorphic or -measures for circle diffeomorphisms were introduced by R.Douady and J.-C. Yoccoz in 1999. They have multiple applications in circle dynamics, with the case $s=-…
Renormalization and scaling of bubbles
Nataliya Goncharuk, Igors Gorbovickis
The paper explores scaling properties of bubbles -- a complex analogue of Arnold tongues, associated to a one-dimensional family of analytic circle diffeomorphisms. Bubbles are smo…
Renormalization of circle maps and smoothness of Arnold tongues
Nataliya Goncharuk, Michael Yampolsky
We study the global behavior of the renormalization operator on a specially constructed Banach manifold that has cubic critical circle maps on its boundary and circle diffeomorphis…
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…
Analytic linearization of conformal maps of the annulus
Nataliya Goncharuk, Michael Yampolsky
We consider holomorphic maps defined in an annulus around in . E. Risler proved that in a generic analytic family of such maps that…
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…
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…
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,…
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…
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…
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…
Complex rotation numbers
Xavier Buff, Nataliya Goncharuk
We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let be an orientation preserving c…