On the Formal Integrability Problem for Planar Differential Systems
We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ℂ2, and impo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/482305 |
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| _version_ | 1832553432057118720 |
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| author | Antonio Algaba Cristóbal García Jaume Giné |
| author_facet | Antonio Algaba Cristóbal García Jaume Giné |
| author_sort | Antonio Algaba |
| collection | DOAJ |
| description | We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions. |
| format | Article |
| id | doaj-art-e074dd22be7d40d8884aa07076cd7f38 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e074dd22be7d40d8884aa07076cd7f382025-02-03T05:54:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/482305482305On the Formal Integrability Problem for Planar Differential SystemsAntonio Algaba0Cristóbal García1Jaume Giné2Departamento de Matemàticas, Facultad de Ciencias, Avda. Tres de Marzo s/n, 21071 Huelva, SpainDepartamento de Matemàticas, Facultad de Ciencias, Avda. Tres de Marzo s/n, 21071 Huelva, SpainDepartamento de Matemàticas, Facultad de Ciencias, Avda. Tres de Marzo s/n, 21071 Huelva, SpainWe study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.http://dx.doi.org/10.1155/2013/482305 |
| spellingShingle | Antonio Algaba Cristóbal García Jaume Giné On the Formal Integrability Problem for Planar Differential Systems Abstract and Applied Analysis |
| title | On the Formal Integrability Problem for Planar Differential Systems |
| title_full | On the Formal Integrability Problem for Planar Differential Systems |
| title_fullStr | On the Formal Integrability Problem for Planar Differential Systems |
| title_full_unstemmed | On the Formal Integrability Problem for Planar Differential Systems |
| title_short | On the Formal Integrability Problem for Planar Differential Systems |
| title_sort | on the formal integrability problem for planar differential systems |
| url | http://dx.doi.org/10.1155/2013/482305 |
| work_keys_str_mv | AT antonioalgaba ontheformalintegrabilityproblemforplanardifferentialsystems AT cristobalgarcia ontheformalintegrabilityproblemforplanardifferentialsystems AT jaumegine ontheformalintegrabilityproblemforplanardifferentialsystems |