  Using a Luttinger liquid description, the correlation function exponents of
various response functions are calculated. Their striking sensitivity to the
non perturbative Wentzel-Bardeen singularity is discussed. For the Hubbard
model coupled to phonons, the equivalent of a phase diagram is established. By
increasing the filling factor towards half filling, the Wentzel-Bardeen
singularity is rapidly approached. This suppresses antiferromagnetic
fluctuations and drives the system in a metallic phase, and ultimately in the
triplet superconducting regime.
