Center problem for systems with two monomial nonlinearities

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2016, American Institute of Mathematical Sciences. All rights reserved. We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. To the best of our knowledge this list includes a new class of Darboux centers that are also persistent centers. The rest of the paper is dedicated to try to prove that the given list is exhaustive. We get several partial results that seem to indicate that this is the case. In particular, we solve the question for several general families with arbitrary high degree and for all cases of degree less or equal than 19. As a byproduct of our study we also obtain the highest known order for weak-foci of planar polynomial systems of some given degrees.
Original languageEnglish
Pages (from-to)577-598
JournalCommunications on Pure and Applied Analysis
Volume15
Issue number2
DOIs
Publication statusPublished - 1 Mar 2016

Keywords

  • Darboux center
  • Holomorphic center
  • Nondegenerate center
  • Persistent center
  • Poincaré-Lyapunov constants
  • Reversible center

Fingerprint Dive into the research topics of 'Center problem for systems with two monomial nonlinearities'. Together they form a unique fingerprint.

Cite this