RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1983

 / 

December

←  →

Reviews of topical problems


Singularities, bifurcations, and catastrophes


V.A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russian Federation

The theories of smooth-mapping singularities and dynamical-system bifurcations are reviewed. Mention is made of the applications to optics (caustic and wave-front metamorphoses) and to theories of short-wave asymptotics, the origin of large-scale structure in the universe, and loss of equilibrium and self-oscillation stability (``catastrophe theory'').

Fulltext pdf (550 KB)
Fulltext is also available at DOI: 10.1070/PU1983v026n12ABEH004581
PACS: 02.30.−f, 03.40.Kf
DOI: 10.1070/PU1983v026n12ABEH004581
URL: https://ufn.ru/en/articles/1983/12/a/
Citation: Arnol’d V I "Singularities, bifurcations, and catastrophes" Sov. Phys. Usp. 26 1025–1037 (1983)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Арнольд В И «Особенности, бифуркации и катастрофы» УФН 141 569–590 (1983); DOI: 10.3367/UFNr.0141.198312a.0569

Cited by (35) ↓ Similar articles (20)

  1. Savvidy G Annals Of Physics 463 169626 (2024)
  2. Julián-Macías I, Martínez-Niconoff G et al J. Opt. Soc. Am. A 41 686 (2024)
  3. Julián-Macías I, Martínez-Niconoff G et al Phys. Scr. 98 085012 (2023)
  4. Krasnov Ya, Rabinowitz I Symmetry 14 2186 (2022)
  5. Rabinowitz I J Math Sci 266 723 (2022)
  6. González-Juárez A, Silva-Ortigoza G, Espíndola-Ramos E J. Opt. 23 015603 (2021)
  7. Donnelly S M, Lopez N A, Dodin I Y Phys. Rev. E 104 (2) (2021)
  8. Krasnov Ya Springer Proceedings In Mathematics & Statistics Vol. Modern Methods in Operator Theory and Harmonic AnalysisSpectral Theory for Nonlinear Operators: Quadratic Case291 Chapter 12 (2019) p. 199
  9. Cabrera-Rosas Omar de J, Sosa-Sánchez C T et al J. Opt. 21 035603 (2019)
  10. González-Juárez A, Silva-Ortigoza G Phys. Scr. 94 055505 (2019)
  11. Julián-Macías I, Rickenstorff-Parrao C et al J. Opt. Soc. Am. A 35 267 (2018)
  12. Ivanitskii G R Phys.-Usp. 61 871 (2018)
  13. Wells G G, Ruiz-Gutiérrez É et al Nat Commun 9 (1) (2018)
  14. Cabrera-Rosas Omar de Jesús, Espíndola-Ramos E et al J. Opt. 19 015603 (2017)
  15. Ivanitskii G R Uspekhi Fizicheskikh Nauk 187 757 (2017) [Ivanitskii G R Phys.-Usp. 60 705 (2017)]
  16. Cabrera-Rosas Omar de Jesús, Espíndola-Ramos E et al J. Opt. 19 055606 (2017)
  17. Neyrinck M C Mon. Not. R. Astron. Soc. 460 816 (2016)
  18. Merkulov V S J. Exp. Theor. Phys. 120 182 (2015)
  19. Rumanov E N Uspekhi Fizicheskikh Nauk 183 103 (2013) [Rumanov E N Phys.-Usp. 56 93 (2013)]
  20. Buchert T, Ostermann M Phys. Rev. D 86 (2) (2012)
  21. Vaganova N I, Rumanov E N Dokl. Phys. 56 507 (2011)
  22. Budagovsky I A, Zolot’ko A S et al J. Exp. Theor. Phys. 111 135 (2010)
  23. Puzynin I V, Boyadzhiev T L et al Phys. Part. Nuclei 38 70 (2007)
  24. Barkovskiĭ L M, Furs A N Opt. Spectrosc. 90 561 (2001)
  25. Vol. Fourth International Kharkov Symposium ’Physics and Engineering of Millimeter and Sub-Millimeter Waves’. Symposium Proceedings (Cat. No.01EX429)Analytical theory of hard excitation in the long-time-interaction O-type resonance oscillatorYu.V.KornienkoD.Masalov2 (2001) p. 577
  26. Brekhovskikh L M, Godin O A Springer Series On Wave Phenomena Vol. Acoustics of Layered Media IIThe Field at and near a Caustic10 Chapter 6 (1999) p. 209
  27. MARSTON PHILIP L Physical Acoustics Vol. 21 (1992) p. 1
  28. Brekhovskikh L M, Godin O A Springer Series On Wave Phenomena Vol. Acoustics of Layered Media IIThe Field at and near a Caustic10 Chapter 6 (1992) p. 194
  29. Comprehensive Chemical Kinetics Vol. Catastrophe TheoryChapter 3 Applications of Elementary Catastrophe Theory (Non-Chemical Systems)33 (1992) p. 77
  30. Isichenko M B Rev. Mod. Phys. 64 961 (1992)
  31. Morozov A Yu Uspekhi Fizicheskikh Nauk 162 83 (1992)
  32. Marmo G, Morandi G, Mukunda N Riv. Nuovo Cim. 13 1 (1990)
  33. Krupkin P L, Nagornykh S N Mater Sci 24 33 (1988)
  34. Chernosatonskii L A, Novikov V V Physics Letters A 117 349 (1986)
  35. Haberman R Wave Motion 8 267 (1986)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions