Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors (Q867352)

Some explicit solutions to \textit{F. Jean}'s recursive equations [ESAIM, Control Optim. Calc. Var. 1, 241--266 (1996; Zbl 0874.93033)] for the study of local behaviours of Goursat flags are deduced. It is shown that one can algorithmically read back the relevant geometric classes from a given growth vector. This gives a secondary Gödel-like super-encoding of the geometric classes of Goursat objects. See also \textit{R. Montgomery} and \textit{M. Zhitomirskii} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 4, 459--493 (2001; Zbl 1013.58004)] and \textit{M. Cheaito} and the author [ESAIM, Control Optim. Calc. Var. 4, 137--158 (1999; Zbl 0957.58002)].