Meandering of trajectories of polynomial vector fields in the affine n-space.

Novikov, Dimitri, and Yakovenko, Sergei. "Meandering of trajectories of polynomial vector fields in the affine n-space.." Publicacions Matemàtiques 41.1 (1997): 223-242. <http://eudml.org/doc/41296>.

@article{Novikov1997,
abstract = {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 closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted or at best indicated.},
author = {Novikov, Dimitri, Yakovenko, Sergei},
journal = {Publicacions Matemàtiques},
keywords = {Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ecuaciones polinómicas; Ideales; Oscilaciones; oscillation; ascending chains; polynomial ideals; zeros of analytic functions},
language = {eng},
number = {1},
pages = {223-242},
title = {Meandering of trajectories of polynomial vector fields in the affine n-space.},
url = {http://eudml.org/doc/41296},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Novikov, Dimitri
AU - Yakovenko, Sergei
TI - Meandering of trajectories of polynomial vector fields in the affine n-space.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 1
SP - 223
EP - 242
AB - 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 closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted or at best indicated.
LA - eng
KW - Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ecuaciones polinómicas; Ideales; Oscilaciones; oscillation; ascending chains; polynomial ideals; zeros of analytic functions
UR - http://eudml.org/doc/41296
ER -