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Topological analysis and synthesis of chaotic time series. (English) Zbl 1194.37135
Summary: We have developed a topological procedure for analyzing chaotic time series which identifies the stretching and squeezing mechanisms responsible for chaotic behavior in low-dimensional dynamical systems. These mechanisms, quantitatively described by a “template” or “knot-holder”, can then be used to model the processes which generate the original chaotic data set.

MSC:
37M10 Time series analysis of dynamical systems
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