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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:199352 |
| Online Access: | https://ddd.uab.cat/record/199352 https://dx.doi.org/urn:doi:10.1080/14689367.2017.1420141 |
| Access Level: | Open access |
| Keyword: | Darboux integrability theory Invariant meridian Invariant parallel N-dimensional spheres |
| Summary: | 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. |
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