On trajectories of analytic gradient vector fields
type: Item
instance of: scholarly article
title: On trajectories of analytic gradient vector fields
zbMATH Open document ID: 1066.58022
author: Aleksandra Nowel
author: Zbigniew Szafraniec
published in: Journal of Differential Equations
publication date: 2002-10-16T00:00:00Z
review text: The main result of the paper is the following Theorem: Let \(f: \mathbb{R}^n\), \(0\to \mathbb{R},\,0\) be a real analytic function defined in some neighbourhood of the origin. The set of non-trivial trajectories of the equation \(\dot x=\nabla f(x)\) attracted by the origin has the same Čech-Alexander cohomology groups as the real Milnor fibre of \(f\).
Mathematics Subject Classification ID: 58K45
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1815480
zbMATH Keywords: analytic gradient vector field
zbMATH Keywords: analytic function
zbMATH Keywords: Čech-Alexander cohomology group
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
OpenAlex ID: W1987302748
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DOI: 10.1006/JDEQ.2001.4142
description: scientific article; zbMATH DE number 1815480