Big denominators and analytic normal forms

In this joint work with M. Zhitomirskii, we study the action of an analytic pseudogroup of transformations on the space of germs of analytic objects such as conformal structures, vector fields, nonisoled singularities...We consider an higher order perturbation $F$ of an homogeneous object $F_0$ and we are interested in the conjugacy problem to a normal form with respect to $F_0$. We prove, that if the cohomological operator (associated to $F_0$) has the Big denominators property and if the space of normal forms is well chosen then there exists an analytic transformation to a normal form. We apply this result to nonisoled singulatities, conformal structures... If these big denominators do not grow fast enough, then we show that there always exists a formal Gevrey solution to the conjugacy problem.