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Fractal Dimensions as Chaos Indicators

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Abstract

The correlation dimension D 2 is used to develop a method of classification for phase space orbits. D 2 depends only on the mutual distances of the orbit’s points, therefore the time development of the orbit is reflected in the time development of the correlation dimension approximants. It is shown, that this technique allows to investigate the dynamical properties of a phase space orbit, a classification of chaotic and regular orbits and a detection of sticky orbits.

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Freistetter, F. Fractal Dimensions as Chaos Indicators. Celestial Mechanics and Dynamical Astronomy 78, 211–225 (2000). https://doi.org/10.1023/A:1011157505026

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  • DOI: https://doi.org/10.1023/A:1011157505026

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