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

Abstract : 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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Lucile Mégret. Studies of the Petrov Module for a Family of Generalized Liénard Integrable Systems. Qualitative Theory of Dynamical Systems, SP Birkhäuser Verlag Basel, 2017, 20 (2), pp.1-21. ⟨10.1007/s12346-017-0250-3⟩. ⟨hal-01571808⟩

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