The study of periodic orbits of dynamical systems. The use of a computer (Q578863)

We examine the role of a computer to prove the existence of periodic orbits of nonquadratic dynamical systems on the lines of the work of \textit{J. G. Sinai} and \textit{E. B. Vul} [ibid. 23, 27-47 (1980; Zbl 0509.34024)] for quadratic systems. We show that, in principle, the work can be successful. Results, simpler in the case of quadratic systems, are applied to the well studied Lorenz model.