The equivalence theory for infinite type hypersurfaces in ℂ²

We develop a classification theory for real-analytic hypersurfaces in C 2 \mathbb {C}^{2} the case when hypersurface is of infinite type at reference point. This remaining, not yet understood Problème local, formulated by H. Poincaré 1907 and asking complete biholomorphic real complex space. One novel aspect our results notion smooth normal forms hypersurfaces. rely fundamentally on recently developed CR-DS technique CR-geometry.