The DOI matches its Crossref record; 70 of the 70 references it cites were found in a registry or an index.
Ergodic theory of chaos and strange attractors
Abstract
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.
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Cites
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Physiological time-series analysis using approximate entropy and sample entropy
Richman, J. S., & Moorman, J. R. (2000) · American Journal of Physiology-Heart and Circulatory Physiology · doi:10.1152/ajpheart.2000.278.6.h2039 · Cited by 7,880
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
Permutation Entropy: A Natural Complexity Measure for Time Series
Bandt, C., & Pompe, B. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.174102 · Cited by 4,867
Multiscale Entropy Analysis of Complex Physiologic Time Series
Costa, M., Goldberger, A. L., & Peng, C.-K. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.068102 · Cited by 3,207
Multiscale entropy analysis of biological signals
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Metadata
- Authors
- Eckmann, J. P., & Ruelle, D.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1985-07-01
- Volume
- 57
- Issue
- 3
- Pages
- 617-656
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W1998727969
- Cited by
- 4,941
- References
- 70
- FWCI
- 111.77
- Type
- journal article
- Language
- en
- Open access
- closed
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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).
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