72 citations · 117 across the 35 of their papers we have counts for
10 papers · 1 filter
Noetherianity and length of Melnikov functions
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
We study foliations in given by polynomial deformations of the form , with a family of cycles. The \emph{Poincaré first return map}…
Nilpotence of Orbits under Monodromy and the Length of Melnikov Functions
Pavao Mardešić, Dmitry Novikov, Laura Ortiz-Bobadilla +1
Let be a polynomial, a non-trivial cycle in a generic fiber of and let be a polynomial -form, thus defining a polynomial d…
Rolle models in the real and complex world
Dmitry Novikov, Sergei Yakovenko
Numerous problems of analysis (real and complex) and geometry (analytic, algebraic, Diophantine e.a.) can be reduced to calculation of the ``number of solutions'' of systems of equ…
Bounding the length of iterated integrals of the first nonzero Melnikov function
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
We consider small polynomial deformations of integrable systems of the form , and the first nonzero term of the displacement function $Δ(t,ε)=\sum…
On global non-oscillation of linear ordinary differential equations with polynomial coefficients
Dmitry Novikov, Boris Shapiro
In this note we show that a linear ordinary differential equation with polynomial coefficients is globally non-oscillating in if and only if it is Fuchsian, and at…
Quasialgebraic Functions
Gal Binyamini, Dmitry Novikov, Sergei Yakovenko
We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated ze…