Bounding the number of zeros of certain Abelian integrals

F. Mañosas, J. Villadelprat

Research output: Contribution to journalArticleResearchpeer-review

51 Citations (Scopus)


In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)1656-1669
JournalJournal of Differential Equations
Publication statusPublished - 15 Sep 2011


  • Abelian integral
  • Chebyshev system
  • Hamiltonian perturbation
  • Limit cycle
  • Wronskian


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