A QUADRATIC SYSTEM WITH A CRITICAL FOCUS OF ORDER 3

Under the guidauce of Prof. Chin Yuanshun, the author has studied a conjecture in the 16th problem of Hilbert’s "there is no limit cycle around a critical focus of order 3". Denoting this conjecture by integrals, we divide it into three cases: (ⅰ) exponential function; (ⅱ) logarithmic function; and (ⅲ) power function. In this letter, it has been proved that the conjecture holds true under case (ⅱ). With regard to (ⅰ) and (ⅲ) we have also obtained some results, which will be given else-