Formal and analytical integrability of the Bianchi IX system

In this paper we provide a complete description of the first integrals of the classical Bianchi IX system that can be described by a general class of formal power series. As a corollary we also obtain a complete description of some of its analytic first integrals in a neighborhood of the origin. In particular, we prove that the system is not completely integrable by analytic first integrals. © 2006 American Institute of Physics.