  It is well known that the dynamics of a Hamiltonian system depends crucially
on whether or not it possesses nonlinear resonances. In the generic case, the
set of nonlinear resonances consists of independent clusters of resonantly
interacting modes, described by a few low-dimensional dynamical systems. We
show that 1) most frequently met clusters are described by integrable dynamical
systems, and 2) construction of clusters can be used as the base for the
Clipping method, substantially more effective for these systems than the
Galerkin method. The results can be used directly for systems with cubic
Hamiltonian.
