Equivalence of the Melnikov Function Method and the Averaging Method

• Maoan Han ^[1] ; Valery G. Romanovski ^[2] ; Xiang Zhang ^[3]
  1. [1] Shanghai Normal University

     Shanghai Normal University

     China

     
  2. [2] University of Maribor

     University of Maribor

     Eslovenia

     
  3. [3] Shanghai Jiao Tong University

     Shanghai Jiao Tong University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 2, 2016, págs. 471-479
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • There is a folklore about the equivalence between the Melnikov method and the averaging method for studying the number of limit cycles, which are bifurcated from the period annulus of planar analytic differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging function, modulo both Melnikov and averaging functions of order less than k, produce the same number of limit cycles of planar analytic (or C∞) near-Hamiltonian systems.