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arXiv · 1702.05495

Darboux theory of integrability for real polynomial vector fields on $\sss^n$

Jaume Llibre·Adrian C. Murza
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Abstract

This is a survey on the Darboux theory of integrability for polynomial vector fields, first in $\R^n$ and second in the $n$-dimensional sphere $\sss^n$. We also provide new results about the maximum number of parallels and meridians that a polynomial vector field $\X$ on $\sss^n$ 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 $\R^n$ can have in function of the degree of $\Y$.

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Jaume Llibre, Adrian C. Murza. 2017-02-17. Darboux theory of integrability for real polynomial vector fields on $\sss^n$. https://arxiv.org/abs/1702.05495

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