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Dokl. Akad. Nauk SSSR, 1977, Volume 234, Number 2, Pages 336–339 (Mi dan40990)  

This article is cited in 16 scientific papers (total in 16 papers)

MATHEMATICAL PHYSICS

On the origin and structure of the Lorenz attractor

V. S. Afraimovich, V. V. Bykov, L. P. Shilnikov

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Gor'kii

Full text: PDF file (663 kB)

Bibliographic databases:
UDC: 53:51+517.91
Presented: А. В. Гапонов-Грехов
Received: 17.12.1976

Citation: V. S. Afraimovich, V. V. Bykov, L. P. Shilnikov, “On the origin and structure of the Lorenz attractor”, Dokl. Akad. Nauk SSSR, 234:2 (1977), 336–339

Citation in format AMSBIB
\Bibitem{AfrBykShi77}
\by V.~S.~Afraimovich, V.~V.~Bykov, L.~P.~Shilnikov
\paper On the origin and structure of the Lorenz attractor
\jour Dokl. Akad. Nauk SSSR
\yr 1977
\vol 234
\issue 2
\pages 336--339
\mathnet{http://mi.mathnet.ru/dan40990}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0462175}
\zmath{https://zbmath.org/?q=an:0451.76052}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. V. Plykin, “On the geometry of hyperbolic attractors of smooth cascades”, Russian Math. Surveys, 39:6 (1984), 85–131  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. A. Pokrovskii, “Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers I”, Theoret. and Math. Phys., 62:2 (1985), 183–196  mathnet  crossref  mathscinet  isi
    3. S. V. Gonchenko, L. P. Shilnikov, “On moduli of systems with a structurally unstable homoclinic Poincare curve”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 417–445  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. E. A. Sataev, “Invariant measures for hyperbolic maps with singularities”, Russian Math. Surveys, 47:1 (1992), 191–251  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. D. V. Turaev, L. P. Shilnikov, “An example of a wild strange attractor”, Sb. Math., 189:2 (1998), 291–314  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, G. I. Strelkova, “Statistical properties of dynamical chaos”, Phys. Usp., 48:2 (2005), 151–166  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    7. S. V. Gonchenko, I. I. Ovsyannikov, “O bifurkatsiyakh trekhmernykh diffeomorfizmov s negrubym geteroklinicheskim konturom, soderzhaschim sedlo-fokusy”, Nelineinaya dinam., 6:1 (2010), 61–77  mathnet  elib
    8. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
    9. E. A. Sataev, “Invariant measures for singular hyperbolic attractors”, Sb. Math., 201:3 (2010), 419–470  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov, “K voprosu o stsenariyakh vozniknoveniya khaosa u trekhmernykh otobrazhenii”, Nelineinaya dinam., 8:1 (2012), 3–28  mathnet
    11. A. S. Gonchenko, S. V. Gonchenko, “O suschestvovanii attraktorov lorentsevskogo tipa v negolonomnoi modeli «keltskogo kamnya»”, Nelineinaya dinam., 9:1 (2013), 77–89  mathnet
    12. A. V. Borisov, A. O. Kazakov, S. P. Kuznetsov, “Nonlinear dynamics of the rattleback: a nonholonomic model”, Phys. Usp., 57:5 (2014), 453–460  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    13. Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov”, Regul. Chaotic Dyn., 19:4 (2014), 435–460  mathnet  crossref  mathscinet  zmath
    14. A. P. Afanas'ev, S. M. Dzyuba, “Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side”, Comput. Math. Math. Phys., 55:10 (2015), 1665–1673  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    15. A. O. Kazakov, A. D. Kozlov, “Nesimmetrichnyi attraktor Lorentsa kak primer novogo psevdogiperbolicheskogo attraktora v trekhmernykh sistemakh”, Zhurnal SVMO, 20:2 (2018), 187–198  mathnet  crossref
    16. G. I. Strelkova, V. S. Anishchenko, “Spatio-temporal structures in ensembles of coupled chaotic systems”, Phys. Usp., 63:2 (2020), 145–161  mathnet  crossref  crossref  isi  elib
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