Center conditions and limit cycles for a class of nilpotent-Poincarè systems

摘要

A class of nilpotent-Poincarè system is discussed in this paper. Center conditions are obtained by methods of inverse integrating factor and theory of rotated vector field. When n>2, we proved that there are 2n+4 small amplitude limit cycles enclosing the origin O(0,0). When n=2, there are 14 limit cycles enclosing the origin O(0,0).