Numerical verification of algebraic non-integrability for high dimensional dynamical systems

The singular point analysis, such as the Painleve test and Yoshida's test, is a computational method and has been implemented in a symbolic computational manner. But, in applying the singular point analysis to high dimensional and/or 'complex' dynamical systems, we face with some computational difficulties. To cope with these difficulties, we propose a new numerical technique of the singular point analysis with the aid of the self-validating numerics. Using this technique, the singular point analysis can now be applicable to a wide class of high dimensional and/or 'complex' dynamical systems, and in many cases dynamical properties such as the algebraic non-integrability can be proven for such systems.