The dynamics near quasi-parabolic fixed points of holomorphic diffeomorphisms in C2

Let F be a germ of holomorphic diffeomorphism of C-2 fixing O and such that dF(O) has eigenvalues 1 and e(itheta) with \e(itheta)\ = 1 and e(itheta) not equal 1. Introducing suitable normal forms for F we define an invariant, nu(F) greater than or equal to 2, and a generic condition, that of being dynamically separating. In the case F is dynamically separating, we prove that there exist nu(F) - 1 parabolic curves for F at O tangent to the eigenspace of 1.