Darboux theory of integrability for polynomial vector fields on d54a;n

Jaume Llibre, Adrian C. Murza

Research output: Contribution to journalArticleResearch

Abstract

© 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.
Original languageEnglish
Pages (from-to)646-659
JournalDynamical Systems
Volume33
DOIs
Publication statusPublished - 2 Oct 2018

Keywords

  • Darboux integrability theory
  • invariant meridians
  • invariant parallels
  • n-dimensional sphere

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