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Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (243) |
SM ISO690:2012 REPEŞCO, Vadim. Qualitative analysis of polynomial differential systems with the line at infinity of maximal multiplicity: exploring linear, quadratic, cubic, quartic, and quintic cases. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2023, nr. 2(16), pp. 111-117. ISSN 2537-6284. DOI: https://doi.org/10.36120/2587-3644.v16i2.111-117 |
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Acta et commentationes (Ştiinţe Exacte și ale Naturii) | ||||||
Numărul 2(16) / 2023 / ISSN 2537-6284 /ISSNe 2587-3644 | ||||||
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DOI:https://doi.org/10.36120/2587-3644.v16i2.111-117 | ||||||
CZU: 517.925 | ||||||
MSC 2010: 34C05. | ||||||
Pag. 111-117 | ||||||
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This article investigates the phase portraits of polynomial differential systems with maximal multiplicity of the line at infinity. The study explores theoretical foundations, including algebraic multiplicity definitions, to establish the groundwork for qualitative analyses of dynamical systems. Spanning polynomial degrees from linear to quintic, the article systematically presents transformations and conditions to achieve maximal multiplicity of the invariant lines at infinity. Noteworthy inclusions of systematic transformations, such as Poincare transformations, simplify analysis and enhance the ´ accessibility of phase portraits. |
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Cuvinte-cheie Polynomial differential system, phase portrait, infinity, multiplicity of an invariant algebraic curve, Poincare transformation, sistem diferențial polinomial, portret fazic, infinit, multiplicitatea curbei algebrice invariante, transformarea Poincaré |
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<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Repeşco, V.F.</dc:creator> <dc:date>2023-12-30</dc:date> <dc:description xml:lang='en'><p>This article investigates the phase portraits of polynomial differential systems with maximal multiplicity of the line at infinity. The study explores theoretical foundations, including algebraic multiplicity definitions, to establish the groundwork for qualitative analyses of dynamical systems. Spanning polynomial degrees from linear to quintic, the article systematically presents transformations and conditions to achieve maximal multiplicity of the invariant lines at infinity. Noteworthy inclusions of systematic transformations, such as Poincare transformations, simplify analysis and enhance the ´ accessibility of phase portraits.</p></dc:description> <dc:description xml:lang='ro'><p>Acest articol investighează portretele de fază ale sistemelor diferențiale polinomiale cu multiplicitatea maximă a liniei de la infinit. Studiul explorează fundamentele teoretice, inclusiv definițiile multiplicității algebrice, pentru a stabili baza pentru analize calitative ale sistemelor dinamice. Acoperind grade polinomiale de la liniar la quintic, articolul prezintă în mod sistematic transformări și condiții pentru a obține multiplicitatea maximală a dreptei invariante de la infinit. Incluziuni notabile ale transformărilor sistematice, cum ar fi transformările Poincaré, simplifică analiza și îmbunătățesc accesibilitatea portretelor de fază.</p></dc:description> <dc:identifier>10.36120/2587-3644.v16i2.111-117</dc:identifier> <dc:source>Acta et commentationes (Ştiinţe Exacte și ale Naturii) 16 (2) 111-117</dc:source> <dc:subject>Polynomial differential system</dc:subject> <dc:subject>phase portrait</dc:subject> <dc:subject>infinity</dc:subject> <dc:subject>multiplicity of an invariant algebraic curve</dc:subject> <dc:subject>Poincare transformation</dc:subject> <dc:subject>sistem diferențial polinomial</dc:subject> <dc:subject>portret fazic</dc:subject> <dc:subject>infinit</dc:subject> <dc:subject>multiplicitatea curbei algebrice invariante</dc:subject> <dc:subject>transformarea Poincaré</dc:subject> <dc:title>Qualitative analysis of polynomial differential systems with the line at infinity of maximal multiplicity: exploring linear, quadratic, cubic, quartic, and quintic cases</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>