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517.925 (42) |
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (243) |
![]() 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 |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
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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