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Embedding as a modeling problem. (English) Zbl 0965.37061
This paper is devoted to embedding as a modeling problem. The practice of embedding relies on a celebrated result of Takens. However there are difficulties with the embedding step of all previous results. Here the authors present an alternative that seems to be powerful and widely applicable. The authors present a modified procedure, nonuniform embedding, which in particular is relevant when there are multiple timescales in the dynamics. Moreover, for more complex nonlinear dynamics the authors introduce a variable embedding, where, in a suitable sense, the embedding changes with the state of the system.

MSC:
37M10 Time series analysis of dynamical systems
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