This concept of rotational factor maps is closely connected to harmonic limits, which are ergodic sums (for discrete-time systems) or integrals (for systems in continuous time). It turns out that the existence of rotational factor maps is equivalent to the existence of non-zero harmonic limits. So we use harmonic limits to analyse the spectral properties of dynamical systems given by the iteration of a map, by a semi-flow or by a control system.
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