  We present a new method of analysis of measure-preserving dynamical systems,
based on frequency analysis and ergodic theory, which extends our earlier work
[1]. Our method employs the novel concept of harmonic time average [2], and is
realized as a computational algorithms for visualization of periodic and
quasi-periodic sets or arbitrary periodicity in the phase space. Besides
identifying all periodic sets, our method is useful in detecting chaotic phase
space regions with a good precision. The range of method's applicability is
illustrated using well-known Chirikov standard map, while its full potential is
presented by studying higher-dimensional measure-preserving systems, in
particular Froeschl\'e map and extended standard map.
