G. D. Birkhoff conjectured [Bull. Soc. Math. Fr. 40, 305-323 (1912; JFM 43.0818.01)] that there exists an analytic differential equation which contains recurrent and non-almost-perodic motions. In 1981 Ding Tongren gave a satisfactory but quite complicated answer to Birkhoff’s conjecture in a hardly available Chinese paper. Using some results of A. S. Besicovitch [Fundam. Math. 28, 61-65 (1937; Zbl 0015.37503) and Proc. Camb. Philos. Soc. 47, 38-45 (1951; Zbl 0054.070)], the present author has constructed a kind of recurrent and non-almost-periodic dynamical system on the torus and hence he has gained a simpler answer to the conjecture.