ON THE CLASSIFICATION OF GENERIC QUADRATIC VECTOR FIELDS WITH NO LIMIT CYCLES

G.T.Santos firstly considered the classification problem on generic quadraticvector fields with no limit cycles.He got 25 subclasses.Cat Suilin addedanother 8 subclasses.However,Cai’s result is also incomplete.There is acrucial question about determining the upper bound of the number of subclasses.In 1980 the author suggested the method of determining the upper bound ofsubclasses of generic quadratic vector fields with no limit cycles at the ThirdConfercnce of Differential Equations in the People’s Republic of China.Inhis preprint of this paper the author showed that there are 65 subclasses atmost.Afterwards[4]found that there are two pairs of subclasses written repeatlyin[3].In 1984 Zu Demin gave 4 new examples whose phase portraits correspondto subclasses 1.9,1.10,1.11 and 2.5.Furthermore Zu provcd that 10 subclasses