Qualitative analysis of polynomial differential systems with the line at infinity of maximal multiplicity: exploring linear, quadratic, cubic, quartic, and quintic cases

This article investigates the phase portraits of polynomial differential systems with maximal multiplicity at the line at infinity. The study explores theoretical foundations, including algebraic multiplicity definitions, to establish the groundwork for qualitative analyses of dynamical systems. Sp...

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Bibliographic Details
Main Author: Vadim Repeșco
Format: Article
Language:English
Published: "Ion Creanga" State Pedagogical University 2024-01-01
Series:Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
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Online Access:https://revistaust.upsc.md/index.php/acta_exacte/article/view/965
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Summary:This article investigates the phase portraits of polynomial differential systems with maximal multiplicity at 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 Poincaré transformations, simplify analysis and enhance the accessibility of phase portraits.
ISSN:2537-6284
2587-3644