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Detecting orbits of high periods from numerical solutions of the Rossler system

For the Rossler system both subharmonic and chaotic motions can be phase coherent. Nevertheless, we can identify such motions of the Rossler system by their low frequency spectra bounded by the average fundamental frequency of unstable period-one orbits. These bounded low-frequency spectra are defined by the Prony method of spectral analysis. Numerical experiments demonstrate that this approach can yield unstable orbits of high periods from chaotic time-series.