Mapping models of invariant scaling. II

For multi-dimensional invariant scaling the existence of a multidimensional scale is established. The one-dimensional components of the scale are correlationally independent. A characteristic equation of the model is introduced whose power increases with the problem dimension. The equation which helps obtain a universal, in the framework of a family of model mappings of different dimensions, representation of the scaling function which leads in the case of singular proximity function in the original feature space to a finite parametric representation of the scaling function. This representation is conducive to computing procedures. A technique is described to obtain an initial approximation of a solution of multidimensional problems whereby the requirement that the characteristic equation be cubic must be met with any dimension of the problem.