Trajectories of polynomial vector fields and ascending chains of polynomial ideals

Dmitri Novikov; Sergei Yakovenko

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 2, page 563-609
  • ISSN: 0373-0956

Abstract

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We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in ℝ n and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coefficients) 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 finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.

How to cite

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Novikov, Dmitri, and Yakovenko, Sergei. "Trajectories of polynomial vector fields and ascending chains of polynomial ideals." Annales de l'institut Fourier 49.2 (1999): 563-609. <http://eudml.org/doc/75347>.

@article{Novikov1999,
abstract = {We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in $\{\Bbb R\}^n$ and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coefficients) 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 finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.},
author = {Novikov, Dmitri, Yakovenko, Sergei},
journal = {Annales de l'institut Fourier},
keywords = {chains of polynomial ideals; intersections; integral curves; polynomial vector field},
language = {eng},
number = {2},
pages = {563-609},
publisher = {Association des Annales de l'Institut Fourier},
title = {Trajectories of polynomial vector fields and ascending chains of polynomial ideals},
url = {http://eudml.org/doc/75347},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Novikov, Dmitri
AU - Yakovenko, Sergei
TI - Trajectories of polynomial vector fields and ascending chains of polynomial ideals
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 2
SP - 563
EP - 609
AB - We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in ${\Bbb R}^n$ and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coefficients) 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 finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.
LA - eng
KW - chains of polynomial ideals; intersections; integral curves; polynomial vector field
UR - http://eudml.org/doc/75347
ER -

References

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