Darboux theory of integrability for real polynomial vector fields on Sⁿ
This is a survey on the Darboux theory of integrability for polynomial vector fields, first in Rⁿ and second in the n-dimensional sphere Sⁿ. We also provide new results about the maximum number of invariant parallels and meridians that a polynomial vector field X on Sⁿ can have in function of its de...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199352 |
| Acceso en línea: | https://ddd.uab.cat/record/199352 https://dx.doi.org/urn:doi:10.1080/14689367.2017.1420141 |
| Access Level: | acceso abierto |
| Palabra clave: | Darboux integrability theory Invariant meridian Invariant parallel N-dimensional spheres |
| Sumario: | This is a survey on the Darboux theory of integrability for polynomial vector fields, first in Rⁿ and second in the n-dimensional sphere Sⁿ. We also provide new results about the maximum number of invariant parallels and meridians that a polynomial vector field X on Sⁿ can have in function of its degree. These results in some sense extend the known result on the maximum number of hyperplanes that a polynomial vector field Y in Rⁿ can have in function of the degree of Y. |
|---|