k-essence and the coincidence problem

k-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behavior of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.