  Searching normal forms for real analytic submanifolds of C^n involves
convergence problems. In 1983, J.K. Moser and S.M. Webster provided examples of
real analytic surfaces in C^2 having an isolated hyperbolic (in the sense of E.
Bishop) complex tangency, which are formally but not holomorphically
normalizable (because of the presence of small divisors), even if the normal
form is itself real analytic or algebraic. On the contrary, it appears that
such a nonconvergence phenomenon does not appear for submanifolds of C^n whose
CR dimension is locally constant, in view of recent results by S.M. Baouendi,
P. Ebenfelt and L.P. Rothschild. These results hold true with hypotheses which
are relatively simple, but satisfied at a Zariski-generic. Notably, these
authors establish that every invertible formal CR mapping between two
submanifolds of C^n which are real analytic, generic, finitely nondegenerate
and minimal (in the sense of J.-M. Tr\'epreau and A.E. Tumanov) is convergent.
In this paper, we establish a more general convergence theorem, which is valid
without any nondegeneracy condition, and which confirms the rigidity of the CR
category (see Theorem 1.23). This result may be interpreted as a formal Schwarz
reflection principle for CR mappings. We deduce that every formal CR
equivalence between two submanifolds of C^n which are real analytic, generic
and minimal is convergent if and only if both submanifolds are holomorphically
nondegenerate (in the sense of N. Stanton). Finally, we establish that two
submanifolds of C^n which are real analytic, generic and minimal are formally
CR equivalent if and only if they are biholomorphically equivalent.
