Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories

19 Sep 2018Boyan XuChristopher J. TralieAlice AntiaMichael LinJose A. Perea

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics. This can be used, for instance, to show that sliding window embeddings of periodic signals recover topological loops, and that sliding window embeddings of quasiperiodic signals recover high-dimensional torii... (read more)

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