ONE METHOD OF CONSTRUCTING POSITIVELY INVARIANT SETS FOR A LORENZ SYSTEM.

An algorithm for constructing positively invariant sets containing separatrices which emerge from the singular zero saddle point O is proposed for a Lorenz system. The domains which contain bifurcation curves corresponding to the existence of separatrix loops of the saddle O in Lorenz's system are estimated. From the estimates obtained, in particular, it follows that when the Prandtl number approaches infinity the area in which there are no separatrix loops from the saddle O increases without limit.