Analysis of the local integrability by methods of normal form and power geometry

A. D. Bruno, V. F. Edneral


Abstract: We consider an autonomous system of ODEs which is solved concerning derivatives. A search of its formal and analytical integrals near its finite stationary point is produced by a usage of its normal form. The infinitely far stationary point at first is moved to finite one by means of a power transformation. This approach is applied to the Yang–Mills system. It is appeared, that in a neighborhood of one infinitely far stationary point this system is locally nonintegrable. That confirms known outcome about global nonintegrability of the system.