Electron - fhonon interaction in the vicinity of a van-hove singularity

The interaction between electrons and acoustic phonons in the vicinity of a Van - Hove singular point is considered. It is shown that even weak interaction leads to a considerable change in the characteristics of the electron gas in the region of the singularity. The electron spectrum changes from quadratic to linear, while the density of states falls off linearly in the neighborhood of the singular point.