Stability of FRW cosmology with a generalized Chaplygin gas

We apply methods of dynamical systems to study the behavior of a universe dominated by the generalized Chaplygin gas. We reduce the dynamics to a two-dimensional Hamiltonian system and study its behavior for various ranges of parameters. The dynamics is studied on the phase plane by using methods of a qualitative analysis of differential equations. The behavior of trajectories at infinity is studied in some convenient coordinates introduced on the phase plane. Hence we show that the Friedmann-Robertson-Walker model with the generalized Chaplygin gas is structurally stable. We clearly find the domains of cosmic acceleration as well as conditions for which the horizon problem is solved. We also define some general class of fluids which generalize the Chaplygin gas. The dynamics of such models in terms of energy conditions is also discussed.