Normalization flow

I propose a new approach to the theory of normal forms for Hamiltonian ODE systems near a non-degenerate equilibrium position. The traditional normalization procedure is performed step-by-step: non-resonant terms in the expansion of the Hamiltonian function are removed first in the lowest degree, then in the next one and so on. I consider the space of all Hamiltonian functions with equilibrium position at the origin and construct a differential equation in this space. Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along the flow of this equation correspond to canonical coordinate changes. So, we have a continuous normalization procedure. The formal aspect of the theory presents no difficulties. The analytic aspect and the problems of convergence of series, as usual, non-trivial.