The weak-Painlevé property as a criterion for the integrability of dynamical-systems

Abstract

We investigate the validity of the weak-Painlevé property as an integrability criterion. We present an example of a time-dependent Hamiltonian system which possesses a weak-Painlevé type expansion, while presenting a chaotic behavior. However, this system presents also critical fixed singularities. The importance of the latter, as far as integrability is concerned, is discussed here.