On the Approximate Polar Curves of Foliations
We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians giv...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/613 |
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| author | Percy Fernández-Sánchez Evelia R. García Barroso Nancy Saravia-Molina |
| author_facet | Percy Fernández-Sánchez Evelia R. García Barroso Nancy Saravia-Molina |
| author_sort | Percy Fernández-Sánchez |
| collection | DOAJ |
| description | We present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by García Barroso and Gwoździewicz for plane branches. |
| first_indexed | 2024-03-11T09:34:55Z |
| format | Article |
| id | doaj.art-f795d230b99d409195103d797aa891de |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:55Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f795d230b99d409195103d797aa891de2023-11-16T17:22:07ZengMDPI AGMathematics2227-73902023-01-0111361310.3390/math11030613On the Approximate Polar Curves of FoliationsPercy Fernández-Sánchez0Evelia R. García Barroso1Nancy Saravia-Molina2Departamento Ciencias—Sección Matemáticas, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel 15088, Lima, PeruDepartamento Matemáticas, Estadística e I.O. Sección de Matemáticas, Universidad de La Laguna, Apartado de Correos 456, 38200 La Laguna, Tenerife, SpainDepartamento Ciencias—Sección Matemáticas, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel 15088, Lima, PeruWe present a decomposition theorem of the generic polar curves of a generalized curve foliation with only one separatrix and the Hamiltonian foliations defined by the approximate roots of the generatrix. This is a generalization to foliations of the decomposition theorem of approximate Jacobians given by García Barroso and Gwoździewicz for plane branches.https://www.mdpi.com/2227-7390/11/3/613non-dicritical foliationpolar curvecharacteristic approximate root |
| spellingShingle | Percy Fernández-Sánchez Evelia R. García Barroso Nancy Saravia-Molina On the Approximate Polar Curves of Foliations Mathematics non-dicritical foliation polar curve characteristic approximate root |
| title | On the Approximate Polar Curves of Foliations |
| title_full | On the Approximate Polar Curves of Foliations |
| title_fullStr | On the Approximate Polar Curves of Foliations |
| title_full_unstemmed | On the Approximate Polar Curves of Foliations |
| title_short | On the Approximate Polar Curves of Foliations |
| title_sort | on the approximate polar curves of foliations |
| topic | non-dicritical foliation polar curve characteristic approximate root |
| url | https://www.mdpi.com/2227-7390/11/3/613 |
| work_keys_str_mv | AT percyfernandezsanchez ontheapproximatepolarcurvesoffoliations AT eveliargarciabarroso ontheapproximatepolarcurvesoffoliations AT nancysaraviamolina ontheapproximatepolarcurvesoffoliations |