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517.925 (42) |
Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (243) |
![]() REPEŞCO, Vadim. Canonical forms of cubic differential systems with real invariant straight lines of total multiplicity seven along one direction. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2018, nr. 2(6), pp. 124-132. ISSN 2537-6284. |
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Acta et commentationes (Ştiinţe Exacte și ale Naturii) | ||||||
Numărul 2(6) / 2018 / ISSN 2537-6284 /ISSNe 2587-3644 | ||||||
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CZU: 517.925 | ||||||
MSC 2010: 34C05 | ||||||
Pag. 124-132 | ||||||
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Consider the general cubic differential system x = P(x, y) , y =Q(x, y) , where [ ] ,,PQx y ÎR , { } max deg ,deg 3 P Q = , ( ) ,1GCDPQ= . If this system has enough invariant straight lines considered with their multiplicities, then, according to [1], we can construct a Darboux first integral. In this paper we obtain 26 canonical forms for cubic differential systems which possess real invariant straight lines along one direction of total multiplicity seven including the straight line at the infinity |
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Cuvinte-cheie Cubic differential system, invariant straight line, Darboux integrability, sistem diferențial cubic, dreaptă invariantă, integrabilitate Darboux |
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<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns='http://datacite.org/schema/kernel-3' xsi:schemaLocation='http://datacite.org/schema/kernel-3 http://schema.datacite.org/meta/kernel-3/metadata.xsd'> <creators> <creator> <creatorName>Repeşco, V.F.</creatorName> <affiliation>Universitatea de Stat din Tiraspol, Moldova, Republica</affiliation> </creator> </creators> <titles> <title xml:lang='en'>Canonical forms of cubic differential systems with real invariant straight lines of total multiplicity seven along one direction</title> </titles> <publisher>Instrumentul Bibliometric National</publisher> <publicationYear>2018</publicationYear> <relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>2537-6284</relatedIdentifier> <subjects> <subject>Cubic differential system</subject> <subject>invariant straight line</subject> <subject>Darboux integrability</subject> <subject>sistem diferențial cubic</subject> <subject>dreaptă invariantă</subject> <subject>integrabilitate Darboux</subject> <subject schemeURI='http://udcdata.info/' subjectScheme='UDC'>517.925</subject> </subjects> <dates> <date dateType='Issued'>2018-12-27</date> </dates> <resourceType resourceTypeGeneral='Text'>Journal article</resourceType> <descriptions> <description xml:lang='en' descriptionType='Abstract'><p>Consider the general cubic differential system <em>x</em> = <em>P</em>(<em>x</em>, <em>y</em>) , <em>y</em> =<em>Q</em>(<em>x</em>, <em>y</em>) , where [ ] ,,<em>PQx y </em>Î<strong>R </strong>, { } max deg ,deg 3 <em>P Q </em>= , ( ) ,1<em>GCDPQ</em>= . If this system has enough invariant straight lines considered with their multiplicities, then, according to [1], we can construct a Darboux first integral. In this paper we obtain 26 canonical forms for cubic differential systems which possess real invariant straight lines along one direction of total multiplicity seven including the straight line at the infinity</p></description> <description xml:lang='ro' descriptionType='Abstract'><p>Fie sistemul diferențial cubic general system <em>x</em> = <em>P</em>(<em>x</em>, <em>y</em>) , <em>y</em> =<em>Q</em>(<em>x</em>, <em>y</em>) , unde [ ] ,,<em>PQx y </em>Î<strong>R </strong>,max{deg<em>P</em>,deg<em>Q</em>} = 3 ,<em>GCD</em>(<em>P</em>,<em>Q</em>) =1. Conform [1], pentru un sistem diferențial cubic se poate de construit o integrală primă de tip Darboux, dacă sistemul dat posedă un număr suficient de drepte invariante considerate cu multiplicitățile lor. În această lucrare se obțin 26 sisteme ce reprezintă formele canonice ale sistemelor diferențiale cubice ce posedă drepte invariante reale de-a lungul unei direcții și a căror multiplicitate totală este egală cu șapte împreună cu dreapta de la infinit.</p></description> </descriptions> <formats> <format>application/pdf</format> </formats> </resource>