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In the paper we discuss certain classes of vector distributions in thetangent bundles to manifolds, obtained by series of applications of theso-called generalized Cartan prolongations (gCp). The classical Cartanprolongations deal with rank-2 distributions and are responsible for theappearance of the Goursat distributions. Similarly, the so-called specialmulti-flags are generated in the result of successive applications of gCp's.Singularities of such distributions turn out to be very rich, although withoutfunctional moduli of the local classification. The paper focuses on special2-flags, obtained by sequences of gCp's applied to rank-3 distributions. Astratification of germs of special 2-flags of all lengths into singularityclasses is constructed. This stratification provides invariant geometricsignificance to the vast family of local polynomial pseudo-normal forms forspecial 2-flags introduced earlier in [Mormul P., Banach Center Publ., Vol. 65,Polish Acad. Sci., Warsaw, 2004, 157-178]. This is the main contribution of thepresent paper. The singularity classes endow those multi-parameter normalforms, which were obtained just as a by-product of sequences of gCp's, with ageometrical meaning.

Singularity Classes of Special 2-Flags