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Geometry from a Time Series
Abstract
It is shown how the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow might be determined experimentally. Techniques are outlined for reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system, and for determining the dimensionality of the system's attractor. These techniques are applied to a well-known simple three-dimensional chaotic dynamical system.
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Citations
Cited by
Determining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Ott, E., Grebogi, C., & Yorke, J. A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1196 · Cited by 5,431
Characterization of Strange Attractors
Grassberger, P., & Procaccia, I. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.346 · Cited by 4,857
Kalman Filtering and Neural Networks
(2001) · Wiley eBooks · doi:10.1002/0471221546 · Cited by 2,386
Metadata
- Authors
- Packard, N. H., Crutchfield, J. P., Farmer, J. D., & Shaw, R. S.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1980-09-01
- Volume
- 45
- Issue
- 9
- Pages
- 712-716
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1984391316
- Cited by
- 3,869
- References
- 0
- FWCI
- 11.60
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Geometry from a Time Series. https://app.cochat.ai/papers/10.1103/physrevlett.45.712
- The paper
- Packard, N. H., Crutchfield, J. P., Farmer, J. D., & Shaw, R. S. (1980). Geometry from a Time Series. Physical Review Letters. https://doi.org/10.1103/physrevlett.45.712
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
