  We study the Landau free energy for a uniaxial ordering, taking into account
two Umklapp terms of comparable strengths (those of the third and fourth
order). Exploring the analogy with the well-known nonintegrable classical
mechanical problem of two mixed nonlinear resonances, we complete the previous
studies of the corresponding phase portrait by calculating numerically periodic
solutions, including those far from the separatrices. It is shown that in the
physical range of parameters only periodic configurations are absolutely
stable. We determine for the first time the complete thermodynamic phase
diagram and show that, in contrast to some earlier claims, the wave number of
the ordering does not pass through the devil's staircase, but through a finite
number of steps which decreases as the amplitudes of the Umklapp terms
increase.
