Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity
The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $\frac{dx}{dt} = P(x,y), \frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent variables and $t$ is the independent variable. The fun...
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| Format: | Article |
| Language: | English |
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"Ion Creanga" State Pedagogical University
2023-09-01
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| 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/895 |
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| _version_ | 1846111918466531328 |
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| author | Vadim Repeșco |
| author_facet | Vadim Repeșco |
| author_sort | Vadim Repeșco |
| collection | DOAJ |
| description |
The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $\frac{dx}{dt} = P(x,y), \frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent variables and $t$ is the independent variable. The functions $P(x,y)$ and $Q(x,y)$ are polynomials in $x$ and $y$. The main objective of this research is to obtain the phase portraits of polynomial differential systems of degree $n\in \{ 3, 4, 5\}$ and having an invariant straight line at the infinity of maximal multiplicity.
%The behaviour of trajectories near the singular points is analysed using various mathematical techniques such as the blow-up method, the Poincaré transformation and other mathematical tools.
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| format | Article |
| id | doaj-art-9a3a46a43a50470d986f25fba2f28356 |
| institution | Kabale University |
| issn | 2537-6284 2587-3644 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | "Ion Creanga" State Pedagogical University |
| record_format | Article |
| series | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
| spelling | doaj-art-9a3a46a43a50470d986f25fba2f283562024-12-22T19:26:10Zeng"Ion Creanga" State Pedagogical UniversityActa et Commentationes: Ştiinţe Exacte şi ale Naturii2537-62842587-36442023-09-0114210.36120/2587-3644.v14i2.68-80895Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinityVadim Repeșco The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $\frac{dx}{dt} = P(x,y), \frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent variables and $t$ is the independent variable. The functions $P(x,y)$ and $Q(x,y)$ are polynomials in $x$ and $y$. The main objective of this research is to obtain the phase portraits of polynomial differential systems of degree $n\in \{ 3, 4, 5\}$ and having an invariant straight line at the infinity of maximal multiplicity. %The behaviour of trajectories near the singular points is analysed using various mathematical techniques such as the blow-up method, the Poincaré transformation and other mathematical tools. https://revistaust.upsc.md/index.php/acta_exacte/article/view/895phase portraitsingular pointPoincare transformation |
| spellingShingle | Vadim Repeșco Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity Acta et Commentationes: Ştiinţe Exacte şi ale Naturii phase portrait singular point Poincare transformation |
| title | Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| title_full | Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| title_fullStr | Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| title_full_unstemmed | Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| title_short | Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| title_sort | phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity |
| topic | phase portrait singular point Poincare transformation |
| url | https://revistaust.upsc.md/index.php/acta_exacte/article/view/895 |
| work_keys_str_mv | AT vadimrepesco phaseportraitsofsomepolynomialdifferentialsystemswithmaximalmultiplicityofthelineattheinfinity |