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A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems
Open accessAbstract
Regular and irregular motions of bounded conservative Hamiltonian systems of N degrees of freedom can be distinguished by the structure of the frequency spectrum of a single trajectory. The spectral entropy S is introduced which provides a measure of the distribution of the frequency components. Numerical calculations on the model Henon and Heiles system and a realistic molecular model are performed. Power spectra are obtained from numerical solutions to Hamilton's equations using fast Fourier transforms and the Hanning method. For regular trajectories S is found to stabilise after a finite time of integration, while for irregular cases S increases erratically. Estimates of the relative volume of regular regions of phase space as a function of energy are given for the two systems.
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Cites
A universal instability of many-dimensional oscillator systems
Chirikov, B. V. (1979) · Physics Reports · doi:10.1016/0370-1573(79)90023-1 · Cited by 4,273
The applicability of the third integral of motion: Some numerical experiments
Hénon, M., & Heiles, C. E. (1964) · The Astronomical Journal · doi:10.1086/109234 · Cited by 2,045
Kolmogorov entropy and numerical experiments
Benettin, G., Galgani, L., & Strelcyn, J.-M. (1976) · Physical Review A · doi:10.1103/physreva.14.2338 · Cited by 1,275
Cited by
Wavelet entropy: a new tool for analysis of short duration brain electrical signals
Rosso, O. A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., & Başar, E. (2001) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(00)00356-3 · Cited by 830
Frozen Gaussians: A very simple semiclassical approximation
Heller, E. J. (1981) · The Journal of Chemical Physics · doi:10.1063/1.442382 · Cited by 746
Forbidden patterns, permutation entropy and stock market inefficiency
Zunino, L., Zanin, M., Tabak, B. M., Pérez, D. G., & Rosso, O. A. (2009) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2009.03.042 · Cited by 249
Combining EEG signal processing with supervised methods for Alzheimer’s patients classification
Fiscon, G., Weitschek, E., Cialini, A., Felici, G., Bertolazzi, P., De Salvo, S., Bramanti, A., Bramanti, P., & De Cola, M. C. (2018) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-018-0613-y · Cited by 172
“We apply the Fast Fourier Transform (FFT) to obtain the spectrum of the EEG signals [37].”
MethodAlzheimer's disease patients classification through EEG signals processing
Fiscon, G., Weitschek, E., Felici, G., Bertolazzi, P., De Salvo, S., Bramanti, P., & De Cola, M. C. (2014) · 2014 IEEE Symposium on Computational Intelligence and Data Mining (CIDM) · doi:10.1109/cidm.2014.7008655 · Cited by 57
Metadata
- Authors
- Powell, G. E., & Percival, I. C.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1979-11
- Volume
- 12
- Issue
- 11
- Pages
- 2053-2071
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2063173250
- Cited by
- 287
- References
- 3
- FWCI
- 6.47
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Powell, G. E., & Percival, I. C. (1979). A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/12/11/017
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