  We address the following question: let F:(R^2,0)->(R^2,0) be an analytic
local diffeomorphism defined in the neighborhood of the non resonant elliptic
fixed point 0 and let \Phi be a formal conjugacy to a normal form N. Supposing
F leaves invariant the foliation by circles centered at 0, what is the analytic
nature of \Phi and N?
