The Herman conjecture part2

This talk is concerned with the convergence of the iteration involved in the Hamiltonian Normal form. The relation between the Hamiltonian Normal Form (HNF) and the Birkhoff Normal form is similar to Padé approximants and Taylor series. I explain why the HNF iteration is convergent over a Cantor set. This is a direct consequence of the Banach functor techniques we introduced with Duco van Straten.