Kolmogorov algorithm for isochronous Hamiltonian systems

We present a Kolmogorov-like algorithm for the computation of normal form in neighborhood an invariant torus `isochronous' Hamiltonian systems, i.e., systems with Hamiltonians $\mathcal{H}=\mathcal{H}_0+\varepsilon \mathcal{H}_1$ where $\mathcal{H}_0$ is $N$ linear oscillators, and $\mathcal{H}_1$ expandable as polynomial series oscillators' canonical variables. This method can be regarded analogue corresponding Lindstedt coupled oscillators. comment on possible use itself under two distinct schemes, one producing analogous to those Birkhoff scheme, another, Kolomogorov scheme which we fix advance frequency torus.