Darboux theory of integrability for real polynomial vector fields on Sⁿ
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Murza, Adrian (Insitutul de Matematică Simion Stoilow al Academiei Române)

Date:	2018
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 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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux integrability theory ; Invariant meridian ; Invariant parallel ; N-dimensional spheres
Published in:	Dynamical Systems, 2018, p. 1-14, ISSN 1468-9375

DOI: 10.1080/14689367.2017.1420141

Postprint 14 p, 779.1 KB

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