  The cosmological dynamics of a quintessence model based on real gas with
general equation of state is presented within the framework of a
three-dimensional dynamical system describing the time evolution of the number
density, the Hubble parameter, and the temperature. Two global first integrals
are found and examples for gas with virial expansion and van der Waals gas are
presented. The van der Waals system is completely integrable. In addition to
the unbounded trajectories, stemming from the presence of the conserved
quantities, stable periodic solutions (closed orbits) also exist under certain
conditions and these represent models of a cyclic Universe. The cyclic
solutions exhibit regions characterised by inflation and deflation, while the
open trajectories are characterised by inflation in a "fly-by" near an unstable
critical point.
