Inventiones Mathematicae Manuscript-nr. an Upper Bound for the Number of Intersections between a Trajectory of a Polynomial Vector Eld and an Algebraic Hypersurface in the N-space ?
نویسنده
چکیده
We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector eld in R n and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coeecients) of the equation and the size of the curve in the space-time, with the exponent depending only on the degree and the dimension. The problem turns out to be closely related to nding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.
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