Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine

Jaume Llibre, Marcelo Messias, Alisson C. Reinol

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)

Abstract

© 2018, Springer-Verlag Italia S.r.l., part of Springer Nature. In this paper we consider all the quadratic polynomial differential systems in R3 having exactly nine invariant planes taking into account their multiplicities. This is the maximum number of invariant planes that these kind of systems can have, without taking into account the infinite plane. We prove that there exist thirty possible configurations for these invariant planes, and we study the realization and the existence of first integrals for each one of these configurations. We show that at least twenty three of these configurations are realizable and provide explicit examples for each one of them.
Original languageEnglish
Pages (from-to)569-580
JournalRendiconti del Circolo Matematico di Palermo
Volume67
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Extactic polynomial
  • First integrals
  • Invariant planes
  • Polynomial differential systems

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