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The Einstein field equations for a class of irrotational non-orthogonallytransitive $G_{2}$ cosmologies are written down as a system of partialdifferential equations. The equilibrium points are self-similar and can bewritten as a one-parameter, five-dimensional, ordinary differential equation.The corresponding cosmological models both evolve and have one-dimension ofinhomogeneity. The major mathematical features of this ordinary differentialequation are derived, and a cosmological interpretation is given. Therelationship to the exceptional Bianchi models is explained and exploited toprovide a conjecture about future generalizations.

classical and quantum gravity

Dynamical Equilibrium States of a Class of Irrotational Non-Orthogonally  Transitive $G_{2}$ Cosmologies I: The Conjecture of Chaotic Cosmological  Inhomogeneity