Bounding the number of zeros of certain Abelian integrals

F. Mañosas, J. Villadelprat

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Abstract

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
Volume251
DOIs
Publication statusPublished - 15 Sep 2011

Keywords

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

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    Mañosas, F., & Villadelprat, J. (2011). Bounding the number of zeros of certain Abelian integrals. Journal of Differential Equations, 251, 1656-1669. https://doi.org/10.1016/j.jde.2011.05.026