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The authors consider the problem of describing the asymptotic states of orthogonal spatially homogeneous cosmologies, near the big bang and late times. They assume perfect fluid source with a linear equation of state and zero cosmological constant. The Einstein field equations are written as an autonomous system of first-order differential equations, so that results from the theory of dynamical systems can be used. The emphasis is on describing certain general properties of the orbits of the differential equations and the local stability of the equilibrium points.
J. Wainwright (Sun,) studied this question.