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( ⃗ k = (1 , 1)). Therefore, near the upper and lower edges of the frequency band, the character of the singularities of the density of states D ( ω ) is universal, D ( ω ) ∝ ( ω − ω$_{0}$ ) near the ω$_{0}$ (see Eq. (13)), and D ( ω ) has a finite jump near the maximal frequency, ω$_{max}$ . At all values of λ , the logarithmic singularity of the form of Δ D ( ω ) = C · ln [ ω$_{c}$/ | ω − ω$_{c}$ | ] is also present (see Fig. 3). 

For large λ , corresponding to a weak interaction of particles, the frequency grows with | ⃗ k | for all directions of ⃗ k . In this case the situation is standard: saddle points are located at four symmetrical points of the type of X (1,0), and only the three aforementioned singularities are present in the density of state function, see Fig. 3a. However, for small λ , λ < λ$_{c}$ = 3 . 6 the dependence ω ( ⃗ k ) for ⃗ k || (0 , 1) is non-monotonous: a local minimum with a standard parabolic 

