Index of an implicit differential equation
type: Item
instance of: scholarly article
title: Index of an implicit differential equation
zbMATH Open document ID: 1192.34012
DOI: 10.5565/PUBLMAT_54110_10
author: L. S. Challapa
author: Maria Aparecida Soares Ruas
published in: Publicacions Matemàtiques
publication date: 2010-02-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pm/1262962139
review text: In the first part of the article, the authors introduce the notion of an index of an implicit ordinary differential equation at an isolated singularity and show that equivalent germs of implicit differential equations possess identical indices. They provide explicit expressions for the case of binary differential equations of degree \(3\). In the second part, these results are applied to study surfaces embedded in \(I\!\!R^5\). An index is introduced for symmetric \(n\)-forms on a surface and related to the Poincaré-Hopf theorem.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 5666218
zbMATH Keywords: implicit differential equation
zbMATH Keywords: index
zbMATH Keywords: binary differential equation
zbMATH Keywords: singularity
Wikidata QID: Q115159254
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5666218