Tracking solutions in tachyon cosmology

We perform a thorough phase-plane analysis of the flow defined by the equations of motion of a FRW Universe filled with a tachyonic fluid plus a barotropic one. The tachyon potential is assumed to be of inverse square form, thus allowing for a two-dimensional autonomous system of equations. The Friedmann constraint, combined with a convenient choice of coordinates, renders the physical state compact. We find the fixed-point solutions, and discuss whether or not they represent attractors. The way the two fluids contribute at late times to the fractional energy density depends on how fast the barotropic fluid redshifts. If it does it fast enough, the tachyonic fluid takes over at late times, but if the opposite happens, the situation will not be completely dominated by the barotropic fluid; instead there will be a residual non-negligible contribution from the tachyon subject to restrictions coming from nucleosynthesis.