Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers. II. Description of trajectories near a separatrix by the matching method

By the method of dividing trajectories into stages and matching them, a theory is developed for constructing asymptotic solutions to Lorenz's system of nonlinear differential equations in the limit of large Rayleigh numbers in a small neighborhood of the zeroth separatrix surface. For this neighborhood, the mapping of Poincar6 successions is obtained and its topological properties described. The use of scaling leads to the finding of a simple succession map without a small parameter describing a large number of bifurcations with increase in the period multiplicity.