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A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems
Open accessAbstract
Based on the Lyapunov characteristic exponents, the ergodic property of dissipative dynamical systems with a few degrees of freedom is studied numerically by employing, as an example, the Lorenz system. The Lorenz system shows the spectra of (+,0,-) type concerning the 1-dimensional Lyapunov exponents, and the exponents take the same values for orbits starting from almost of all initial points on the attractor. This result suggests that the ergodic property for general dynamical systems not necessarily belonging to the category of the axiom-A may also be characterized in the framework of the spectra of the Lyapunov characteristic exponents.
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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
The synchronization of chaotic systems
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00137-0 · Cited by 2,764
Dynamic link of memory—Chaotic memory map in nonequilibrium neural networks
Tsuda, I. (1992) · Neural Networks · doi:10.1016/s0893-6080(05)80029-2 · Cited by 353
Different ways to turbulence in dissipative dynamical systems
Manneville, P., & Pomeau, Y. (1980) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(80)90013-5 · Cited by 305
Silk, D., Kirk, P. D. W., Barnes, C. P., Toni, T., Rose, A., Moon, S., Dallman, M. J., & Stumpf, M. P. H. (2011) · Nature Communications · doi:10.1038/ncomms1496 · Cited by 76
Metadata
- Authors
- Shimada, I., & Nagashima, T.
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1979-06-01
- Volume
- 61
- Issue
- 6
- Pages
- 1605-1616
- ISSN
- 0033-068X (ISSN-L)
- 1347-4081
- OpenAlex
- W2121065739
- Cited by
- 1,040
- References
- 0
- FWCI
- 9.96
- Type
- journal article
- Language
- en
- Open access
- bronze
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