The center and cyclicity problems for quartic linear-like reversible systems

Leonardo P.C. da Cruz, Valery G. Romanovski, J. Torregrosa

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1 Citation (Scopus)


© 2019 Elsevier Ltd In this paper we study a family of quartic linear-like reversible polynomial systems having a nondegenerate center at the origin. This family has degree one with respect to one of the variables. We are interested in systems in this class having two extra nondegenerate centers outside the straight line of symmetry. The geometrical configuration of these centers is aligned or triangular. We solve the center problem in both situations and, in the second case, we study the limit cycles obtained from a simultaneous degenerate Hopf bifurcation in the quartic polynomials class.
Original languageEnglish
Article number111593
Number of pages19
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 1 Jan 2020


  • Center cyclicity
  • Center-focus problem
  • Linear-like reversible centers
  • Quartic centers


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