Multiscale time averaging, Reloaded

We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary order. Here, we consider as an example the problem of finite dimensional conservative dynamical system, which is quasiperiodic and dominated by slow frequencies, leading to small divisor problems in perturbative schemes.