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Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes
Open accessAbstract
The connection between one-dimensional dynamical laws generating discrete processes and their invariant densities as well as their stationary correlaton functions is discussed. In particular the changes occuring under a special equivalence transformation are considered. Correlation functions are used to describe the gradual transition from periodic states to chaotic states via periodic motions with superimposed nonlinearity noise.
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Cites
A collection of mathematical problems
Ulam, S. M. (1960) · Medical Entomology and Zoology · Cited by 2,262
Ergodic problems of classical mechanics
Arnol'd, V. I., & Avez, A. (1968) · Cited by 2,018
Halmos, P. R. (1956) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,083
Ergodic Transformations from an Interval Into Itself
Li, T.-Y., & Yorke, J. A. (1978) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1978-0457679-0 · Cited by 249
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Fluctuations and simple chaotic dynamics
Crutchfield, J. P., Farmer, J. D., & Huberman, B. A. (1982) · Physics Reports · doi:10.1016/0370-1573(82)90089-8 · Cited by 481
Chaos-based random number generators-part I: analysis [cryptography]
Stojanovski, T., & Kocarev, L. (2001) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/81.915385 · Cited by 371
Static parametric fluctuations give nonstatistical behavior in uncoupled chaotic systems
Pérez, G., & Cerdeira, H. A. (1994) · Physical Review E · doi:10.1103/physreve.49.r15 · Cited by 332
Statistics of chaotic binary sequences
Kohda, T., & Tsuneda, A. (1997) · IEEE Transactions on Information Theory · doi:10.1109/18.567654 · Cited by 275
Metadata
- Authors
- Grossmann, S., & Thomae, S.
- Venue
- Zeitschrift für Naturforschung A
- Publisher
- Walter de Gruyter GmbH
- Published
- 1977-12-01
- Volume
- 32
- Issue
- 12
- Pages
- 1353-1363
- ISSN
- 0340-4811 (ISSN-L)
- 1865-7109
- 0932-0784
- OpenAlex
- W1995638437
- Cited by
- 397
- References
- 4
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Grossmann, S., & Thomae, S. (1977). Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes. Zeitschrift für Naturforschung A. https://doi.org/10.1515/zna-1977-1204
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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