Abstract
In this chapter, we introduce the concept of the embedding dimension, as the smallest topological dimension required to ensure that an object described by simpler (often scalar) time series can be embedded in a higher topological dimension.
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References
Antoulas, A.: Mathematical System Theory—The Influence of R. E. Kalman. Springer, Berlin (1991). https://doi.org/10.1007/978-3-662-08546-2
Cover, T., Thomas, J.: Elements of Information Theory. Wiley, London (1991)
Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656 (1985). https://doi.org/10.1103/RevModPhys.57.617
Letellier, C.: Fortran code for estimating the minimum embedding dimension (2013). http://www.atomosyd.net/spip.php?article128
Ruskeepaa, H.: Chaotic data: Delay time and embedding dimension. Wolfram Demonstrations Project (2017)
Takens, F.: Dynamical systems and turbulence. In: Lecture Notes in Mathematics, vol. 898, chap. Detecting Strange Attractors in Turbulence, pp. 366–381. Springer, Berlin (1981)
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Orlando, G., Stoop, R., Taglialatela, G. (2021). Embedding Dimension and Mutual Information. In: Orlando, G., Pisarchik, A.N., Stoop, R. (eds) Nonlinearities in Economics. Dynamic Modeling and Econometrics in Economics and Finance, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-70982-2_7
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DOI: https://doi.org/10.1007/978-3-030-70982-2_7
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