  The classical and quantum mechanics of isolated, nonlinear resonances in
integrable systems with N>=2 degrees of freedom is discussed in terms of
geometry in the space of action variables. Energy surfaces and frequencies are
calculated and graphically presented for invariant tori inside and outside the
resonance zone. The quantum mechanical eigenvalues, computed in the
semiclassical WKB approximation, show a regular pattern when transformed into
the action space of the associated symmetry reduced system: eigenvalues inside
the resonance zone are arranged on N-dimensional cubic lattices, whereas those
outside are, in general, non-periodically distributed. However, N-dimensional
triclinic (skewed) lattices exist locally. Both kinds of lattices are joined
smoothly across the classical separatrix surface. The statements are
illustrated with the help of two and three coupled rotors.
