this paper, concerns oscillatory properties of functions defined by polynomial ordinary differential equations. Geometrically the question is about the number of isolated intersections between an integral curve of a polynomial vector field and an algebraic hypersurface in the Euclidean n-space
Let $K$ be a number field or the function field of a curve over an algebraically closed field of cha...
AbstractWe give an upper bound for the maximum number N of algebraic limit cycles that a planar poly...
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
We give an explicit upper bound for the number of isolated intersections between an integral curve o...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
Abstract. An elementary example shows that the number of zeroes of a component of a solution of a sy...
Abstract. The number of zeroes of the restriction of a given polynomial to the trajectory of a polyn...
Let ξ be a polynomial vector field on $^n$ with coefficients of degree d and P be a polynomial of de...
For a Lipschitzian vector field in IRn, angular velocity of its trajectories with respect to any sta...
problems with deep significance for the advance of mathematical science. There has been intensive re...
Bezout's theorem gives the degree of intersection of two properly intersecting algebraic varieties. ...
Bombieri and Pila gave sharp estimates for the number of integer points $(m,n)$ on a given arc of a ...
17 pagesInternational audienceLet $S$ be a closed orientable hyperbolic surface, and let $\mathcal{O...
Anyone familiar with systems of polynomial equations (whether they majored in math or just had to so...
Let $K$ be a number field or the function field of a curve over an algebraically closed field of cha...
AbstractWe give an upper bound for the maximum number N of algebraic limit cycles that a planar poly...
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
We give an explicit upper bound for the number of isolated intersections between an integral curve o...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
Abstract. We give an explicit upper bound for the number of isolated inter-sections between an integ...
Abstract. An elementary example shows that the number of zeroes of a component of a solution of a sy...
Abstract. The number of zeroes of the restriction of a given polynomial to the trajectory of a polyn...
Let ξ be a polynomial vector field on $^n$ with coefficients of degree d and P be a polynomial of de...
For a Lipschitzian vector field in IRn, angular velocity of its trajectories with respect to any sta...
problems with deep significance for the advance of mathematical science. There has been intensive re...
Bezout's theorem gives the degree of intersection of two properly intersecting algebraic varieties. ...
Bombieri and Pila gave sharp estimates for the number of integer points $(m,n)$ on a given arc of a ...
17 pagesInternational audienceLet $S$ be a closed orientable hyperbolic surface, and let $\mathcal{O...
Anyone familiar with systems of polynomial equations (whether they majored in math or just had to so...
Let $K$ be a number field or the function field of a curve over an algebraically closed field of cha...
AbstractWe give an upper bound for the maximum number N of algebraic limit cycles that a planar poly...
We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial v...
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