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Galoisian obstructions to integrability of Hamiltonian systems. II. (English) Zbl 1140.37354
Summary: By applying the results of our previous paper [ibid. 8, No. 1, 33–95 (2001; Zbl 1140.37352)], we obtain non-integrability results for the following four Hamiltonian systems: the Bianchi IX Cosmological Model, the Sitnikov system of celestial mechanics, the Spring-Pendulum system and a generalization of the homogeneous potentials considered by Yoshida. All these systems are considered over the complex domain (complex time and complex phase space) and the integrability is considered in the Liouville sense of existence of a maximal number of first integrals in involution.

37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
70H07 Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics
34M99 Ordinary differential equations in the complex domain
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