Integrability of Hamiltonian systems and transseries expansions (Q543323)

Analytic Liouville-nonintegrability and smooth Liouville-integrability for 2D Hamiltonian systems are the subjects of this paper having as starting point the study of \textit{G. Gorni} and \textit{G. Zampieri} [Differ. Geom. Appl. 22, No. 3, 287--296 (2005; Zbl 1080.37061)]. The main tools are given by the monodromy property of a certain subsystem of the given Hamiltonian system and by the transseries expansion of a first integral. Asymptotic properties and the Borel summability method for transseries are used several times.