72 citations · 117 across the 35 of their papers we have counts for
38 papers
Complex cells in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
We extend the theory of complex cells introduced by Binyamini and Novikov to the sharply o-minimal setting, obtaining cellular preparation and parameterization theorems which are p…
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…
Infinitesimal and tangential 16-th Hilbert problem on zero-cycles
J. L. Bravo, P. Mardesic, D. Novikov +1
In this paper, given two polynomials and of one variable and a -cycle of , we consider the deformation . We define two functions: the displacement function…
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…
Wilkie's conjecture for Pfaffian structures
Gal Binyamini, Dmitry Novikov, Benny Zack
We prove an effective form of Wilkie's conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height lying in the transcen…