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Attractor: the set of points to which the trajectories of a dynamical system converges over time.
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Lagged variables plot: a plot of a time series as a function of the same time series lagged by multiples of a length of time
$\tau$ . For instance, the axes of a three-dimensional lagged variable plot are the original time series$X(t)$ , the lagged time series$X(t + \tau)$ , and$X(t + 2\tau)$ . -
State space reconstruction: the process of making a representation of a state space of interest that preserves some important properties. In the context of EDM, the reconsctructed state space corresponds to the lagged variables plot of a time series.
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Shadow Manifold: the projection of the original manifold (which is an attractor in our case) into an Euclidean space. This space has a dimension (the embedding dimension) that ensures a one-to-one map to the original manifold.
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Embedding dimension: for our purposes, the dimension of the Euclidean space used to build the shadow manifold. In the case of a state space reconstruction, the embedding dimension is the dimension of this space, that is, the number of axes of the lagged variables plot.