Symbolic Dynamical Resolution of Power Spectra

Abstract

Power spectra have been for a long time employed as a means for the characterization of experimental time signals. After the discovery of low-dimensional chaotic behaviour in physical systems the analysis of power spectra contributed to the detailed understanding of transitions to chaos by period-doubling and quasiperiodicity ¹. However, their usefulness for the investigation of typical chaos has been questioned, since they are not invariant under smooth coordinate changes ¹. Here we show that power spectra are characterized by the topological and the metric properties of symbolic orbits, together with the actual numerical values of the observable. The former two ingredients are dynamical invariants and affect the spectra much more deeply than the latter one, which is obviously non-invariant.