© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. 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.
|Publication status||Published - 2 Oct 2018|
- Darboux integrability theory
- invariant meridians
- invariant parallels
- n-dimensional sphere