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Nelin. Dinam., 2012, Volume 8, Number 1, Pages 3–28 (Mi nd300)  

This article is cited in 18 scientific papers (total in 18 papers)

Towards scenarios of chaos appearance in three-dimensional maps

A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov

Research Institute for Applied Mathematics and Cybernetics, Ulyanova st.  10, Nizhnii Novgorod, 603605, Russia

Keywords: strange attractor, chaotic dynamics, spiral attractor, torus-chaos, homoclinic orbit, invariant curve, three-dimensional Hénon map

Full text: PDF file (4455 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.9
MSC: 37C70, 37C29, 37G25
Received: 06.10.2011

Citation: A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov, “Towards scenarios of chaos appearance in three-dimensional maps”, Nelin. Dinam., 8:1 (2012), 3–28

Citation in format AMSBIB
\Bibitem{GonGonShi12}
\by A.~S.~Gonchenko, S.~V.~Gonchenko, L.~P.~Shilnikov
\paper Towards scenarios of chaos appearance in three-dimensional maps
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 1
\pages 3--28
\mathnet{http://mi.mathnet.ru/nd300}


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    This publication is cited in the following articles:
    1. A. S. Gonchenko, S. V. Gonchenko, A. O. Kazakov, “O nekotorykh novykh aspektakh khaoticheskoi dinamiki «keltskogo kamnya»”, Nelineinaya dinam., 8:3 (2012), 507–518  mathnet
    2. Borisov A.V., Jalnine A.Yu., Kuznetsov S.P., Sataev I.R., Sedova J.V., “Dynamical Phenomena Occurring Due to Phase Volume Compression in Nonholonomic Model of the Rattleback”, Regul. Chaotic Dyn., 17:6 (2012), 512–532  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. S. P. Kuznetsov, A. Yu. Zhalnin, I. R. Sataev, Yu. V. Sedova, “Fenomeny nelineinoi dinamiki dissipativnykh sistem v negolonomnoi mekhanike «keltskogo kamnya»”, Nelineinaya dinam., 8:4 (2012), 735–762  mathnet
    4. A. P. Kuznetsov, S. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, “Stsenarii Landau–Khopfa v ansamble vzaimodeistvuyuschikh ostsillyatorov”, Nelineinaya dinam., 8:5 (2012), 863–873  mathnet
    5. A. S. Gonchenko, S. V. Gonchenko, “O suschestvovanii attraktorov lorentsevskogo tipa v negolonomnoi modeli «keltskogo kamnya»”, Nelineinaya dinam., 9:1 (2013), 77–89  mathnet
    6. A. S. Gonchenko, “Ob attraktorakh lorentsevskogo tipa v modeli keltskogo kamnya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 2, 3–11  mathnet
    7. 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
    8. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
    9. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “The reversal and chaotic attractor in the nonholonomic model of Chaplygin's top”, Regul. Chaotic Dyn., 19:6 (2014), 718–733  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. 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
    11. A. Gonchenko, S. Gonchenko, A. Kazakov, D. Turaev,, “Simple scenarios of onset of chaos in three-dimensional maps”, J. Bifur. Chaos Appl. Sci. Engrg., 24:8 (2014), 1440005, 25 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Gonchenko S.V., Ovsyannikov I.I., Tatjer J.C., “Birth of Discrete Lorenz Attractors At the Bifurcations of 3D Maps With Homoclinic Tangencies to Saddle Points”, Regul. Chaotic Dyn., 19:4 (2014), 495–505  crossref  isi
    13. Gonchenko A.S., Gonchenko S.V., “Retracted: Lorenz-Like Attractors in a Nonholonomic Model of a Rattleback (Retracted Article. See Vol. 30, Pg. C3-C3, 2017)”, Nonlinearity, 28:9 (2015), 3403–3417  crossref  isi
    14. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
    15. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref
    16. A. S. Gonchenko, S. V. Gonchenko, “Variety of strange pseudohyperbolic attractors in three-dimensional generalized Henon maps”, Physica D, 337 (2016), 43–57  crossref  isi
    17. M. Mammeri, “A large chaotic region in a 3-D sinusoid discrete map”, Int. J. Appl. Math. Stat., 55:3 (2016), 133–144  isi
    18. S. Gonchenko, I. Ovsyannikov, “Homoclinic tangencies to resonant saddles and discrete Lorenz attractors”, Discret. Contin. Dyn. Syst.-Ser. S, 10:2 (2017), 273–288  crossref  mathscinet  zmath  isi  scopus
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