GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS

We consider the geometric and algebraic properties of the first-order differential equation on smooth finite-dimensional real manifolds. An affine connection without torsion is compared with a differential flow (autonomic or non-autonomic) on a manifold, with all the original trajectories being some...

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Main Authors:	Забелина Светлана Борисовна, Марченко Татьяна Андреевна, Матвеев Олег Александрович, Пинчук Ирина Александровна
Format:	Article
Language:	Russian
Published:	Moscow Region State University Editorial Office 2019-12-01
Series:	Вестник московского государственного областного университета. Серия: Физика-математика
Subjects:	systems of ordinary differential equations smooth manifolds affine connections universal algebras quasi-groups
Online Access:	http://vestnik-mgou.ru/Articles/View/13383

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spelling	doaj-c5f3b6a7cb3d4aa09a02786839568d212020-11-24T21:52:58ZrusMoscow Region State University Editorial OfficeВестник московского государственного областного университета. Серия: Физика-математика2310-72512019-12-01261310.18384/2310-7251-2019-2-6-13GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDSЗабелина Светлана БорисовнаМарченко Татьяна АндреевнаМатвеев Олег АлександровичПинчук Ирина АлександровнаWe consider the geometric and algebraic properties of the first-order differential equation on smooth finite-dimensional real manifolds. An affine connection without torsion is compared with a differential flow (autonomic or non-autonomic) on a manifold, with all the original trajectories being some geodesic lines of this affine connection. Using differential-algebraic characteristics of affine connectivity, we study some classes of first-order equations on smooth finite-dimensional real differentiable manifolds.http://vestnik-mgou.ru/Articles/View/13383systems of ordinary differential equationssmooth manifoldsaffine connectionsuniversal algebrasquasi-groups
collection	DOAJ
language	Russian
format	Article
sources	DOAJ
author	Забелина Светлана Борисовна Марченко Татьяна Андреевна Матвеев Олег Александрович Пинчук Ирина Александровна
spellingShingle	Забелина Светлана Борисовна Марченко Татьяна Андреевна Матвеев Олег Александрович Пинчук Ирина Александровна GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS Вестник московского государственного областного университета. Серия: Физика-математика systems of ordinary differential equations smooth manifolds affine connections universal algebras quasi-groups
author_facet	Забелина Светлана Борисовна Марченко Татьяна Андреевна Матвеев Олег Александрович Пинчук Ирина Александровна
author_sort	Забелина Светлана Борисовна
title	GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS
title_short	GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS
title_full	GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS
title_fullStr	GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS
title_full_unstemmed	GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS
title_sort	geometric and algebraic properties of first-order differential equations on smooth finite-dimensional real manifolds
publisher	Moscow Region State University Editorial Office
series	Вестник московского государственного областного университета. Серия: Физика-математика
issn	2310-7251
publishDate	2019-12-01
description	We consider the geometric and algebraic properties of the first-order differential equation on smooth finite-dimensional real manifolds. An affine connection without torsion is compared with a differential flow (autonomic or non-autonomic) on a manifold, with all the original trajectories being some geodesic lines of this affine connection. Using differential-algebraic characteristics of affine connectivity, we study some classes of first-order equations on smooth finite-dimensional real differentiable manifolds.
topic	systems of ordinary differential equations smooth manifolds affine connections universal algebras quasi-groups
url	http://vestnik-mgou.ru/Articles/View/13383
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GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS

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