Studies of the Petrov Module for a Family of Generalized Liénard Integrable Systems

• Mégret, Lucile ^[1]
  1. [1] Pierre and Marie Curie University

     Pierre and Marie Curie University

     París, Francia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 3, 2018, págs. 519-539
• Idioma: inglés
• DOI: 10.1007/s12346-017-0250-3
• Enlaces
  • Texto completo
• Resumen

  • In this article we use the Lambert function in order to study a family of integrable generalized Liénard equations Xf which display a center. We first prove a conjugation lemma inside a continuum of nested periodic orbits. Then we deduce an explicit operator of Gelfand–Leray associated with the Hamiltonian of equation Xf. Afterwards, we provide a generating family for the associated Petrov module. Finally, by using the Lambert function, we study the monotonicity of the Abelian integral of this generating family’s elements.

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