On exceptional directions of a homogeneous polynomial system of the second degree

The article considers a homogeneous polynomial three-dimensional system. The method of limit sets is used to study exceptional directions in the vicinity of an isolated singular point of the system. The method is developed differently from the transformation introduced in the works of other authors. As a result, the number of exceptional directions of the system is obtained, corresponding to special points such as anti- saddle, saddle, discovery, saddle-node.