Abstract
Particles within a stochastic—or chaotic—web in phase space can be accelerated to high energies even by weak magnetic fields, and the properties of the web show similarities to the quasicrystal state. Examples of webs with five- and sevenfold symmetries are given. The establishment of stochastic webs and structural coverings of the phase plane may yield new and unexpected results.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Fermi, E., Phys. Rev. 75, 1169–1174 (1949).
Fermi, E., Pasta, J. R. & Ulam, S. Studies of Nonlinear Problems (Los-Alamos Rept LA-1940, 1955).
Filonenko, N. N., Sagdeev, R. Z. & Zaslavsky, G. M. Nuclear Fusion 7, 253–266 (1967).
Zaslavsky, G. M. & Filonenko, N. N. Zh. éksp. teor. Fiz. 54, 1590–1602 (1968).
Arnold, V. I. Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1979).
Arnold, V. I. Dokl. Akad. Nauk SSR 156, 9–12 (1964).
Zaslavsky, G. M. Zh. éksp. teor. Fiz. 88, 1984–1995 (1985).
Zaslavsky, G. M. & Chernikov, A. A. Zh. éksp. teor. Fiz. 89, 1632–1647 (1985).
Zaslavsky, G. M., Zakharov, M. Yu., Sagdeev, R. Z., Usikov, D. A. & Chernikov, A. A. Zh. éksp. teor. Fiz. 91, 500–516 (1986).
Shechtman, D., Blech, J., Gratias, D. & Chan, J. W. Phys. Rev. Lett. 53, 1951–1953 (1984).
Nelson, D. R. & Halperin, B. I. Science 229, 233–238 (1985).
Zaslavsky, G. M., Zakharov, M. Yu., Sagdeev, R. Z., Usikov, D. A. & Chernikov, A. A. Piśma Zh éksp. teor. Fiz. 44, 349–353 (1986).
Penrose, R. Bull. Inst. Math. Applics 10, 266–271 (1974).
Sagdeev, R. Z. & Shapiro, V. D. Piśma Zh. éksp. teor. Fiz. 17, 389–393 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chernikov, A., Sagdeev, R., Usikov, D. et al. Minimal chaos and stochastic webs. Nature 326, 559–563 (1987). https://doi.org/10.1038/326559a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/326559a0
This article is cited by
-
Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates
Scientific Reports (2024)
-
The heteroclinic and codimension-4 bifurcations of a triple SD oscillator
Nonlinear Dynamics (2024)
-
Chaotic electron diffusion through stochastic webs enhances current flow in superlattices
Nature (2004)
-
Forced secondary resonances at the 3 : 1 commensurability
Celestial Mechanics & Dynamical Astronomy (1994)
-
Chaotic streamlines in pre-turbulent states
Nature (1989)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
