Abstract
Dynamical systems for hypersurface homogeneous and hypersurface self-similar models with non-null symmetry surfaces are derived. The equations are cast in a geometric form based on properties of the symmetry surfaces that emphasize the close connection between the various models. Perfect fluid models are discussed in particular. It is shown how the models form a hierarchical structure where simpler models act as building blocks for more complicated ones. Expressions for the fluid's kinematic properties are given and discussed in the context of various special cases.
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