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
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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.