Issues

 / 

1992

 / 

August

←  →

Reviews of topical problems


Finite-dimensional spatial disorder

 a, ,
a Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

The article discusses a new branch of the theory of disorder: the origin, stability and diagnostics of deterministic spatial chaos, i.e., the disorder that can be generated by a dynamical system. Problems are posed, some of which are solved.

Fulltext pdf (1.3 MB)
Fulltext is also available at DOI: 10.1070/PU1992v035n08ABEH002253
PACS: 61.44.Br, 61.30.Cz (all)
DOI: 10.1070/PU1992v035n08ABEH002253
URL: https://ufn.ru/en/articles/1992/8/a/
Citation: Rabinovich M I, Fabrikant A L, Tsimring L Sh "Finite-dimensional spatial disorder" Sov. Phys. Usp. 35 (8) 629–649 (1992)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Рабинович М И, Фабрикант А Л, Цимринг Л Ш «Конечномерный пространственный беспорядок» УФН 162 (8) 1–42 (1992); DOI: 10.3367/UFNr.0162.199208a.0001

References (58) ↓ Cited by (33) Similar articles (20)

  1. Ziman J M Models Of Disorder (Cambridge: Cambridge University Press, 1979); ’?’?р’?’?’?’?, ’O’?’?’?’?’? ’Kzh. ’a’?’?’?’?’? ’?’?с’?’?рya’?’?’? (’a.: ’a’?р, 1982)
  2. White R.M., Geballe ’n.’v. Long Range Order In Solid (New York: Academic Press, 1979); ’?’?р’?’?’?’?, Bumm P., ’I’?’?’?’?’? ’n. ’K’?’?ь’?’?’? ’?’?рya’?’?’? ’? т’?’?р’?ыkh т’?’?’?kh (’a.: ’a’?р, 1982)
  3. ’G’?’?ch-’Gру’?’?’?ch ’E. ’K. ’? ’?р. ’e’?’?’?тр’?’?’?’?ya т’?’?р’?ya ’?’?у’?’?рya’?’?ch’?’?’?ыkh ’?’?’?у’?р’?’?’?’?’?’?’?’?’? (’a.: ’v’?у’?’?, 1981)
  4. ’eфр’?с ’B.’’. ’s’?’?’?’?’? ’? ’?’?’?’?’?тр’?ya ’?’?с’?’?рya’?’?’? (’a.: ’v’?у’?’?, 1982)
  5. Aranson I.S., Rabinovich M.I., Suschik M.M. Chaos And Order In Nature (Ed. H Haken) (Berlin: Springer, 1981) p. 54
  6. Gorshkov K.A., Ostrovsky L.A., Papko V.V., Pikovsky A.S. Phys. Lett. A 74 177 (1979)
  7. Janssen ’n., Janner A. Adv. Phys. 36 519 (1987)
  8. Ashraff J.A., Luck J.;M., Stinchcombe R.B. Phys. Rev. B 41 4314 (1990)
  9. Chernikov A.A., Sagdeev R.Z., Usikov D.A., Zasnavsky G.F. Phys. Lett. A 125 101 (1987)
  10. ’’’?’?’?’?у ’’.’K. Dokl. Akad. Nauk SSSR 44 339 (1944)
  11. Hopf E Comm. Pure. Appl. Math. 1 3031 (1948)
  12. Ecktnann J.P., Procaccia I. Nonlinearity 4 542 (1991)
  13. de Gennes P G The Physics Of Liquid Crystals (Oxford: Clarendon, 1974); Kai S., Chizumi N.. Kohno M. Phys. Rev. A 40 6554 (1989)
  14. Mayer-Kress A (Ed.) Dimensions And Entropies In Chaotic Systems (Berlin: Springer-Verlag, 1986)
  15. Brandstater A et al. Phys. Rev. Lett. 51 1442 (1983)
  16. Glass L., Mackey M.C. From Clocks To Chaos. The Rhythms Of Life (Princeton: Univ. Press, 1988)
  17. Babcock K.L., Westervelt R.M. Phys. Rev. A 40 2022 (1989); Babcock K.L., Westervelt R.M. Phys. Rev. Lett. 64 2168 (1990)
  18. J. Opt. Am. Soc. 66 (1990), Special issue
  19. Grassberger P., Schreber ’n., Schaffrath C. Int. J. Of Bifurcation And Chaos 1 (3) 521 (1991); Casdagli M., Eubank S., Farmer J.D., Gibson J. Physica D 51 52 (1991)
  20. Doerring C.R., Gibbon J.D., Holm D.D., Nicolaenko B. Nonlinearity 1 279 (1988)
  21. Constantin P., Foias C., Nicolaenko ’E., ’n’?т’?’?’? R. Appl. Math. Sci. Ser. Vol. 70 (New York: Springer, 1988)
  22. Afraimovich V.S., Ezehsky A.B., Rabinovich M.I., Zheleznyak A.L., Sheresnevsky M.A. Phyisca D (1992), in press
  23. Mane R Dynamical Systems And Turbulence (Warwich, 1980); Mane R Lecture Notes In Math. Vol. 898 (1981) p. 366
  24. Procaccia L, Grassberger P., Hehtschel H.G.E. Lect. Notes In Physics Vol. 179 (1983) p. 212
  25. Ruelle D Proc. R. Soc. Lond A 427 241 (1990)
  26. Elliot J., Dober P. The Symmetry In Physics Vol. 1, 2 (1980); ’?’?р’?’?’?’?, ’e’?’?’?’?т ’Kzh., ’K’?’?’?р ’’. ’l’?’?’?’?тр’?ya ’? ф’?’?’?’?’? Т. 1, 2 (’a.: ’a’?р, 1983)
  27. Richtmyer R D Principles Of Advanced Mathematical Physics Vol. 2 (New York: Springer-Verlag, 1981); ’?’?р’?’?’?’?, ’i’?khт’?’?’?’?р P. ’zр’?’?ts’?’?ы с’?’?р’?’?’?’?’?’?’? ’?’?т’?’?’?т’?ch’?с’?’?’? ф’?’?’?’?’? Т. 2 (’a.: ’a’?р, 1984)
  28. Ottino J M The Kinematics Of Mixing, Stretching, Chaos, And Transport (Cambridge: Univ. Press, 1989)
  29. ’s’?’?’?’?’?’? ’i., ’’’?’?т’?’? ’i., ’lэ’?’? M. ’s’?’?’?’?’?’?’?’?с’?’?’? ’?’?’?ts’?’? ’?’? ф’?’?’?’?’? (’a.: ’a’?р, 1965)
  30. Swift J., Hohenberg P.C. Phys. Rev. A 15 319 (1977); ’I’?т’?’?’?’? ’B.’E. Usp. Fiz. Nauk 161 (9) 1 (1991); Getling A V Sov. Phys. Usp. 34 737 (1991)
  31. Pomeau Y., Manneville P. J. De Phys. Lett. 40 609 (1979)
  32. ’i’?’?’?’?’?’?’?ch ’a.’R., ’lуshch’?’? ’a.’a. Usp. Fiz. Nauk 160 1 (1990); Rabinovich M, Sushchik M Sov. Phys. Usp. 33 1 (1990)
  33. ’I’?’?’?’?’?’?;’Iр’?kh’?’? ’B.’E., ’’’?’?’?’? ’B.’l., ’dс’?’?’?’? ’I.’E., ’i’?’?’?’?’?’?’?ch ’a.’R. ’v’?’?’?’?’?’?’?ы’? ’?’?’?’?ы (’z’?’? р’?’?. ’B.’E. ’I’?’?’?’?’?’?’?-’Iр’?kh’?’?’?, ’a.’R. ’i’?’?’?’?’?’?’?ch’?) (’a.: ’v’?у’?’?, 1989) p. 61
  34. Bodenschatz E., de Bruyn J.R., Ahlers G., Cennell D. "Experiments on Three Systems With Non-Variational Aspects" Preprint Santa Barbara (1991)
  35. Newell A.C., Whitehead J.A. J. Fluid Mech. 38 279 (1969); Segel L A J. Fluid Mech. 38 203 (1969)
  36. ’G’?’?’?’?’? ’F., ’i’?’?’?’?’?’?’?ch ’a.’R., Zh’?’?’?’?’?ya’? ’B.’’. "’e’?’?’?yuts’?’?’?’?’?сть ’?’?’?’?ch’?’?’?’?р’?’?’?’? ’?’?с’?’?рya’?’?’? ’? CGLE", ’?’?т’?’?’?тсya ’? ’?’?ch’?т’?
  37. Perz-Garcia ’l., Cerisier ’i., ’dсс’?lli R. Propagation In Systems Far From Equilibrium (Eds. J.E. Wesfreid, H.R. Brand, P. Manneville, G. Albinet, N. Boccara) (Berlin: Springer-Verlag, 1988)
  38. ’F’?р’?’?’?’?’? ’’., ’i’?’?’?’?’?’?’?ch ’a.’R., Ts’?’?р’?’?’? ’’.Sh. "’e’?’?’?yuts’?’?’?’?’?сть ’?р’?стр’?’?ст’?’?’?’?’?’?’? ’?’?с’?’?рya’?’?’? ’? ’?р’?’?’?’?’?т’?ыkh ’?’?’?’?’?yakh" ’zр’?’?р’?’?т ’R’z’s ’i’B’v (’v. ’v’?’?’?’?р’?’?, 1992)
  39. Devaney R J. Diffefent. Equat. 21 431 (1976)
  40. Gorshkov K.A., Ostrovsky L.A. Physica D 3 428 (1981)
  41. Aranson I.S., Gorshkov K. A., Lomov A.S., Rabinovich M.I. Physica D 43 (1990)
  42. ’I’?’?’?’?’?’?;’Iр’?kh’?’? A.B., ’’’?’?’?’? ’B.’l., ’i’?’?’?’?’?’?’?ch ’a.’R. ’z’?сь’?’? Zh’e’n’s 44 224 (1986)
  43. Bodenschatz E et al. New Trends In Nonlinear Dynamics And Pattern-Forming Phenomena (The Geometry Of Nonequilibrium, Eds. P. Boullet, Huerre) (New York: Plenum Press, 1988) p. 111
  44. Korslnov L., Rabinovich M.I., Tsimring L.Sh. Phys. Rev. A, submuted
  45. Coullet P., Lega J. Phys. Rev. Lett. 65 1353 (1990)
  46. ’M’?’?рс’?’?’? ’B.’G., ’i’?’?’?’?’?’?’?ch ’a.’R., ’i’?ут’?’? ’E.’z., ’lт’?р’?’?’?’?’?ts ’R.’a. Zh. Eksp. Teor. Fiz. 91 2070 (1986)
  47. Gaponov-Grekhov A.V., Rabinovich M.I. Phys. Today (July) 30 (1990)
  48. ’O’?’?ь’?’?’?’?ch Ya.’G., ’a’?’?ch’?’?’?’? ’l.’B., ’iу’?’?’?’?’?’?’? ’B.’B., ’l’?’?’?’?’?’? ’K.’K. Usp. Fiz. Nauk 152 3 (1987)
  49. Bazhenov M.V., Rabinovich M.I., Fabrikant A.L. Phys. Lett. A (1992)
  50. Afraitnovich V.S., Tsimring L.Sh. "Finite-Dimensional Disorder in Chains of Maps" Preprint UCSD (IAP, 1992)
  51. Shereshevsky M A J. Nonlin. Sci. 1 (2) 206 (1991)
  52. ’i’?’?’?’?’?’?’?ch ’a.’R., ’lуshch’?’? ’a.’a., ’O’?’?’?’?’? ’B.’G. ’s’B’d 26 (12) (1990)
  53. Williamson C H K J. Fluid Mech. 206 579 (1989)
  54. Schreber ’n., Gressberger P. Phys. Lett. A 160 411 (1991)
  55. Meyer C.W., Ahlers G., Callell D.S. Phys. Rev. A 44 2514 (1991)
  56. Quyand Q., Swinney H.L. Chaos 1 411 (1991)
  57. Auyag ’n., Kuramioto Y. Phys. Lett. A 155 410 (1991)
  58. ’dс’?’?’?’? ’I.’E., ’i’?’?’?’?’?’?’?ch ’a.’R., Ts’?’?р’?’?’? ’’.Sh. "’l’?’?khр’?’?’?’?’?ts’?ya ’? kh’?’?с ’? ’?’?’?’?’?’?-’?’?’?’?’?’?р’?’?’?’?’? ts’?’?’?ch’?’? ’?’?’?-’?’?р-’?’?’?’?’?с’?’?kh ’?’?’?’?р’?т’?р’?’?" ’zр’?’?р’?’?т ’R’z’s ’i’B’v (’v. ’v’?’?’?’?р’?’?, 1992)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions