ar X iv : h ep - t h / 06 06 03 2 v 1 5 J un 2 00 6 Exponential Potentials and Attractor Solution of Dilatonic Cosmology

We present phase-plane analysis of cosmologies containing a dilatonic scalar field coupling to a baryotropic fluid with an exponential potential. We show that for baryotropic fluid being radiation the properties of critical points are the same as the conventional scalar field in Ref[11]. For baryotropic fluid being ordinary matter there are coupling between dilatonic scalar field and ordinary matter and therefore the properties of critical points are more distinctive. It is possible for all the critical points to be stable as long as the parameters λ and β satisfy some conditions. We plot the phase plane for some values of λ and β which show the attractor behaviors of the plane-autonomous system clearly. Finally with the bound on β from the observation we conclude that present accelerating expansion is not the eventual stage of universe.