Web geometry of a system of first-order autonomous ordinary differential equations
type: Item
instance of: scholarly article
title: Web geometry of a system of first-order autonomous ordinary differential equations
zbMATH Open document ID: 1333.53023
author: Mehdi Nadjafikhah
author: Rohollah Bakhshandeh Chamazkoti
published in: Journal of Dynamical and Control Systems
publication date: 2015-10-15T00:00:00Z
review text: Using Elie Cartan's method the authors consider elementary properties of a system of autonomous ordinary differential equations with respect to a pseudo-group of the so-called web transformations. Reviewer's remarks: 1) The authors use the term ``web geometry'' but it is not clear, what ``web'' they refer to. One can attach different webs to a given system of ordinary differential equations, and there is the concrete pseudo-group of admissible transformations for every type of these webs. See about them in [\textit{A. A. Duyunova}, Russ. Math. 56, No. 2, 37--49 (2012; Zbl 1257.53020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 2, 43--56 (2012); J. Math. Sci., New York 177, No. 5, 654--667 (2011; Zbl 1290.53019); translation from Fundam. Prikl. Mat. 16, No. 2, 13--31 (2010)]. 2) In Section 2 (The Cartan Equivalence Method), instead of the \(\omega^i\) symbol it is necessary to use \(\omega_i\), since it is the contravariant object. 3) On the left of equation (2.5) there has to be zero. 4) Theorems 1 and 2 are not connected to the content of the article.
Mathematics Subject Classification ID: 53A55
Mathematics Subject Classification ID: 58A15
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 53A60
zbMATH DE Number: 6494572
zbMATH Keywords: Cartan equivalence problem
zbMATH Keywords: web transformations
zbMATH Keywords: autonomous ordinary differential equations
zbMATH Keywords: normalization
zbMATH Keywords: Lorentz system
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
Wikidata QID: Q115383681
full work available at URL: s10883-014-9249-0
OpenAlex ID: W2011290390
cites work: Q5816741
cites work: Q3995740
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cites work: Feedback equivalence of control systems
cites work: Q4849745
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cites work: Ordinary differential equations and dynamical systems
DOI: 10.1007/S10883-014-9249-0
description: scientific article; zbMATH DE number 6494572