Simpler cases arise in locally rotationally-symmetric (LRS) models, where a non-trivial isotropy subgroup is assumed. Here, only two independent parameters and remain, where only one, e.g., can take both signs if discrete gauge freedom is fixed, and the vacuum difference equation is, e.g., for Bianchi I, and  for the correction of a typo). This leads to a reduction between fully anisotropic and isotropic models with only two independent variables, and provides a class of interesting systems to analyze effects of anisotropies. In , for instance, anisotropies are treated perturbatively around isotropy as a model for the more complicated of inhomogeneities. This shows that non-perturbative equations are essential for the singularity issue, while perturbation theory is sufficient to analyze the dynamical behavior of semiclassical states.
Also here, can be scale dependent, resulting in non-equidistant difference equations, which in the case of several independent variables are only rarely transformable to equidistant form . A special case where this is possible is studied in .
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