On the extensions of the Darboux theory of integrability

Jaume Giné, Maite Grau, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

Recently some extensions of the classical Darboux integrability theory to autonomous and non-autonomous polynomial vector fields were completed. The classical Darboux integrability theory and its recent extensions are based on the existence of algebraic invariant hypersurfaces. However the algebraicity of the invariant hypersurfaces is not necessary and the unique necessary condition is the algebraicity of the cofactors associated to them. In this paper a more general extension of the classical Darboux integrability theory is established. © 2013 IOP Publishing Ltd & London Mathematical Society.
Original languageEnglish
Pages (from-to)2221-2229
JournalNonlinearity
Volume26
Issue number8
DOIs
Publication statusPublished - 1 Aug 2013

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