A chebyshev criterion for abelian integrals

M. Grau, F. Manosas, J. Villadelprat

Research output: Contribution to journalArticleResearchpeer-review

87 Citations (Scopus)

Abstract

We present a criterion that provides an easy sufficient condition in order for a collection of Abelian integrals to have the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced. © 2010 American Mathematical Society.
Original languageEnglish
Pages (from-to)109-129
JournalTransactions of the American Mathematical Society
Volume363
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • Abelian integral
  • Chebyshev system
  • Hamiltonian perturbation
  • Limit cycle
  • Planar vector field

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