Darboux theory of integrability for real polynomial vector fields on \sssⁿ

2017/02/17 by Llibre, Jaume, Murza, Adrian C.
#34C05 #34C07 #34C40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.05495

Abstract

This is a survey on the Darboux theory of integrability for polynomial vector fields, first in \Rⁿ and second in the n-dimensional sphere \sssⁿ. We also provide new results about the maximum number of parallels and meridians that a polynomial vector field \X on \sssⁿ 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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