In the present paper that region, in which the (minimal) attractor is situated, is localized in the phase space of the Lorenz system by means of Lyapunov’s second method. Being based on these estimations and the results of paper Differ. Uravn. 22, 1642-1644 (1986; Zbl 0616.34052
) a sufficient condition is given that separatrix loops of the saddle
are missing. Comparison of the bounds for the attractor obtained analytically in this paper shows that for certain parameter regions these estimations practically can not be augmented.