The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real andâ€¦ (More)

We study the local topological structure of generic multijet preimages of algebraic varieties and prove their stratifiability with additional quantitative estimates. The result is a necessaryâ€¦ (More)

We derive an explicit system of Picardâ€“Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that theâ€¦ (More)

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equationsâ€¦ (More)

can have ? This problem is usually referred to as the weakened 16th Hilbert problem (see Hilbert [15], Arnold [1, p.313]). Suppose that the foliation defined on the real plane by {df = 0} posseses aâ€¦ (More)

The presence of human cytomegalovirus (HCMV) in male genital tract suggests its vertical transmission with spermatozoa and the development of a potentially dangerous fetal infection. The objective ofâ€¦ (More)

One of the main results of this paper is an upper bound for the total number of real isolated zeros of complete Abelian integrals, exponential in the degree of the form (Theorem 1 below). This resultâ€¦ (More)

We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane. The problem turns out to be closelyâ€¦ (More)

We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound,â€¦ (More)

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of suchâ€¦ (More)