In this interesting paper the author gives the characterization of Arnold-Mather type for stable singular Legendre immersions in connection with the classification problem. The most important building block of the theory is providing a module structure on the space of infinitesimal integral deformations by means of the notion of natural liftings of differential systems and of contact Hamiltonian vector fields.
The obtained results are directly connected to the following author’s papers: Ann. Inst. Fourier 33, 199–217 (1983; Zbl 0488.58004); Math. Proc. Camb. Philos. Soc. 111, 103–112 (1992; Zbl 0761.58015); Kodai Math. J. 17, 442–451 (1994; Zbl 0828.58005); Banach Cent. Publ. 33, 93–104 (1996; Zbl 0853.58018); Invent. Math. 126, 215–234 (1996; Zbl 0869.58002); J. Geom. Phys. 52, 113–126 (2004; Zbl 1080.58025) and Q. J. Math. 54, 73–102 (2003; Zbl 1049.58039) (jointly with S. Janeczko).