RSS feeds
РусскийEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1988

 / 

October

←  →

Reviews of topical problems


Minimal chaos, stochastic webs, and structures of quasicrystal symmetry

, , ,

The relationship between the problem of the symmetry of a plane tiling and the properties of nonintegrable dynamic systems is reviewed. The formation of stochastic layers and a stochastic web in the motion of linear and nonlinear oscillators subjected to a perturbation is discussed in detail. Emphasis is placed on research on the symmetry properties of a stochastic web with a fractal structure of a quasicrystal type. Structures with a quasicrystal symmetry form as a result of an interaction of two types of symmetries: translational and rotational. Various characteristics of structures with a quasicrystal symmetry are discussed: the distributions of stable and unstable points, the state density, and the Fourier spectrum. Quasicrystal structures in solid state physics, hydrodynamics, botany, and ornamental art are discussed.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1988v031n10ABEH005632
PACS: 61.44.Br, 05.45.Df (all)
DOI: 10.1070/PU1988v031n10ABEH005632
URL: https://ufn.ru/en/articles/1988/10/a/
Citation: Zaslavskii G M, Sagdeev R Z, Usikov D A, Chernikov A A "Minimal chaos, stochastic webs, and structures of quasicrystal symmetry" Sov. Phys. Usp. 31 887–915 (1988)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Заславский Г М, Сагдеев Р З, Усиков Д А, Черников А А «Минимальный хаос, стохастическая паутина и структуры с симметрией типа „квазикристалл“» УФН 156 193–251 (1988); DOI: 10.3367/UFNr.0156.198810a.0193

References (83) Cited by (58) ↓ Similar articles (20)

  1. Kuznetsov A P, Sedova Yu V, Stankevich N V Int. J. Bifurcation Chaos 33 (15) (2023)
  2. Sokolov I V, Sun H et al Journal Of Computational Physics 476 111923 (2023)
  3. Karimov A I, Butusov D N et al 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM), (2017) p. 341
  4. Roth J J. Phys.: Condens. Matter 29 184003 (2017)
  5. Akram M Ja, Saif F Nonlinear Dyn 83 963 (2016)
  6. Kuznetsov A P, Sedova Yu V Int. J. Bifurcation Chaos 26 1630019 (2016)
  7. Bakunin O G Uspekhi Fizicheskikh Nauk 185 271 (2015) [Bakunin O G Phys.-Usp. 58 252 (2015)]
  8. Kells G A, Twamley J, Heffernan D M Chaos, Solitons & Fractals 36 772 (2008)
  9. Loskutov A Yu Uspekhi Fizicheskikh Nauk 177 989 (2007)
  10. Arnold’s Problems Chapter 2 (2005) p. 181
  11. Kveglis L I, Kuzovnikov A V, Timofeev I V Proceedings. 2005 International Conference Physics and Control, 2005., (2005) p. 742
  12. Spektor R, Choueiri E Y Phys. Rev. E 69 (4) (2004)
  13. Litvak-Hinenzon A, Rom-Kedar V Physica D: Nonlinear Phenomena 164 213 (2002)
  14. Yudin V V, Pisarenko T A et al Crystallogr. Rep. 47 189 (2002)
  15. Kveglis L I, Jarkov S M, Staroverova I V Phys. Solid State 43 1543 (2001)
  16. Lowenstein J H, Vivaldi F 10 747 (2000)
  17. Eleonsky V M, Korolev V G, Kulagin N E J. Phys. A: Math. Gen. 33 2469 (2000)
  18. Lowenstein J, Hatjispyros S, Vivaldi F 7 49 (1997)
  19. Dana I, Kalisky T Phys. Rev. E 53 R2025 (1996)
  20. Chia P-K, Schmitz L, Conn R W 3 1545 (1996)
  21. Chia P-K, Schmitz L, Conn R W 3 1569 (1996)
  22. Galashev A E J Struct Chem 37 120 (1996)
  23. Fasoli A, Lister J B et al Phys. Rev. Lett. 76 1067 (1996)
  24. Rom A Y, Fishman S et al Phys. Rev. B 54 9819 (1996)
  25. Lowenstein J H Nonlinearity 9 1071 (1996)
  26. Lowenstein J H 5 566 (1995)
  27. Fasoli A, Lister J B et al Nucl. Fusion 35 1485 (1995)
  28. Kozhevnikov A A Phys. Rev. D 52 6043 (1995)
  29. Lowenstein J H 4 397 (1994)
  30. Lowenstein J H Phys. Rev. E 49 232 (1994)
  31. Fasoli A, Skiff F et al Phys. Rev. Lett. 70 303 (1993)
  32. Yannacopoulos A N, Rowlands G J. Phys. A: Math. Gen. 26 6231 (1993)
  33. Lowenstein J H Phys. Rev. E 47 R3811 (1993)
  34. Rom-Kedar V, Kadanoff L P et al Physica D: Nonlinear Phenomena 62 51 (1993)
  35. Yannacopoulos A N, Rowlands G Physica D: Nonlinear Phenomena 65 71 (1993)
  36. Yannacopoulos A N, Rowlands G Physica D: Nonlinear Phenomena 57 355 (1992)
  37. Oliveira e Silva L, Mendonça J T Phys. Rev. A 46 6700 (1992)
  38. Lowenstein J H 2 413 (1992)
  39. Alekseev K N, Alekseeva N V J. Phys. B: At. Mol. Opt. Phys. 25 1949 (1992)
  40. Rax J M 4 3962 (1992)
  41. Amick C, Ching E S C et al J Nonlinear Sci 2 9 (1992)
  42. Hoveijn I Chaos, Solitons & Fractals 2 81 (1992)
  43. Zaslavsky G M NATO ASI Series Vol. Microscopic Aspects of Nonlinearity in Condensed MatterFrom Chaos to Quasicrystals264 Chapter 6 (1991) p. 83
  44. Yannacopoulos A N, Rowlands G Physics Letters A 155 133 (1991)
  45. Lowenstein J H 1 473 (1991)
  46. Karelin A I J Struct Chem 32 199 (1991)
  47. Lowenstein J H Phys. Rev. A 43 4104 (1991)
  48. Afanasiev V V, Sagdeev R Z, Zaslavsky G M 1 143 (1991)
  49. Zaslavsky G M 1 1 (1991)
  50. Sagdeev R Z, Zaslavsky G M New Perspectives in Turbulence Chapter 14 (1991) p. 349
  51. Chaĭkovsky D K, Zaslavsky G M 1 463 (1991)
  52. Szydlowski M, Łapeta A Gen Relat Gravit 23 151 (1991)
  53. Babalievski F, Peshev O Computer Physics Communications 60 27 (1990)
  54. Szydłowski M, Ł;apeta A Physics Letters A 148 239 (1990)
  55. Afanasiev V V, Chernikov A A et al Physics Letters A 144 229 (1990)
  56. Afanas’ev V V, Sagdeev R Z et al Physics Letters A 151 276 (1990)
  57. Carioli S M, Chernikov A A, Neishtadt A I Phys. Scr. 40 707 (1989)
  58. Beloshapkin V V, Chernikov A A et al Nature 337 133 (1989)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions