Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity
In this paper the quartic differential systems with a center-focus critical point and non-degenerate infinity are examined. We show that in this family the maximal multiplicity of an affine invariant straight line is six. Modulo the affine transformation and time rescaling the classes of systems wit...
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| Format: | Article |
| Language: | English |
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"Ion Creanga" State Pedagogical University
2025-01-01
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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/1085 |
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| _version_ | 1823857395807289344 |
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| author | Olga Vacaraș |
| author_facet | Olga Vacaraș |
| author_sort | Olga Vacaraș |
| collection | DOAJ |
| description | In this paper the quartic differential systems with a center-focus critical point and non-degenerate infinity are examined. We show that in this family the maximal multiplicity of an affine invariant straight line is six. Modulo the affine transformation and time rescaling the classes of systems with an affine invariant straight line of multiplicity two, three,..., six are determined. In the cases when the quartic systems has an affine invariant straight line of maximal multiplicity the problem of the center is solved. |
| format | Article |
| id | doaj-art-027a903b3d35488899328ef28096f905 |
| institution | Kabale University |
| issn | 2537-6284 2587-3644 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | "Ion Creanga" State Pedagogical University |
| record_format | Article |
| series | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
| spelling | doaj-art-027a903b3d35488899328ef28096f9052025-02-11T21:03:58Zeng"Ion Creanga" State Pedagogical UniversityActa et Commentationes: Ştiinţe Exacte şi ale Naturii2537-62842587-36442025-01-0118210.36120/2587-3644.v18i2.38-54Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicityOlga Vacaraș0Technical University of Moldova, 9/8 Studen\c{t}ilor St., Chi\c sin\u au, Republic of MoldovaIn this paper the quartic differential systems with a center-focus critical point and non-degenerate infinity are examined. We show that in this family the maximal multiplicity of an affine invariant straight line is six. Modulo the affine transformation and time rescaling the classes of systems with an affine invariant straight line of multiplicity two, three,..., six are determined. In the cases when the quartic systems has an affine invariant straight line of maximal multiplicity the problem of the center is solved.https://revistaust.upsc.md/index.php/acta_exacte/article/view/1085quartic differential systemmultiple invariant linecenter-focus critical point |
| spellingShingle | Olga Vacaraș Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity Acta et Commentationes: Ştiinţe Exacte şi ale Naturii quartic differential system multiple invariant line center-focus critical point |
| title | Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| title_full | Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| title_fullStr | Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| title_full_unstemmed | Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| title_short | Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| title_sort | center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity |
| topic | quartic differential system multiple invariant line center-focus critical point |
| url | https://revistaust.upsc.md/index.php/acta_exacte/article/view/1085 |
| work_keys_str_mv | AT olgavacaras centerproblemforquarticdifferentialsystemswithanaffineinvariantstraightlineofmaximalmultiplicity |