Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems (Q1094895)

The paper presents a detailed review of the relation between integrability of a system and the analytic properties of the solution of the equations of motion in the complex time plane. Three different approaches are considered: Yoshida's method [e.g.: \textit{H. Yoshida}, Celestial Mech. 31, 381-399 (1983; Zbl 0556.70015)], the ``weak Painlevé'' approach and Ziglin's method [e.g.: \textit{S. L. Ziglin}, Funkts. Anal. Prilozh. 17, No.1, 8-23 (1983; Zbl 0518.58016)]. Among others, the authors derive an extension of Ziglin's theorem on nonintegrability.