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

Dimitri Novikov; Sergei Yakovenko

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 1, page 223-242
- ISSN: 0214-1493

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topNovikov, 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 -

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