4 citations · 7 across the 5 of their papers we have counts for
6 papers
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,…
Sternberg linearization theorem for skew products
Yulij Ilyashenko, Olga Romaskevich
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even…
Total rigidity of generic quadratic vector fields
Yulij Ilyashenko, Vadims Moldavskis
We consider a class of foliations on the complex projective plane that are determined by a quadratic vector field in a fixed affine neighborhood. Such foliations, as a rule, have a…
A restricted version of the Hilbert's 16th problem for quadratic vector fields
Yulij Ilyashenko, Jaume Llibre
The restricted version of the Hilbert 16th problem for quadratic vector fields requires an upper estimate of the number of limit cycles through a vector parameter that characterize…
Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces
Yulij Ilyashenko
An upper bound of the variation of argument of a holomorphic function along a curve on a Riemann surface is given. This bound is expressed through the Bernstein index of the functi…
Restricted version of the infinitesimal Hilbert 16th problem
A. A. Glutsyuk, Yu. S. Ilyashenko
The paper deals with the {\it infinitesimal Hilbert 16th problem}: to find an upper estimate of the number of zeros of an Abelian integral regarded as a function of a parameter. In…