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Dokl. Akad. Nauk, 1993, Volume 329, Number 4, Pages 404–407 (Mi dan5235)  

This article is cited in 10 scientific papers (total in 10 papers)

MATHEMATICS

On the existence of Newhouse regions in a neighborhood of systems with a structurally unstable homoclinic Poincaré curve (the multidimensional case)

S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Full text: PDF file (339 kB)

English version:
Doklady Mathematics, 1993, 47:2, 268–273

Bibliographic databases:
UDC: 517.9
Presented: Я. Г. Синай
Received: 15.09.1992

Citation: S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “On the existence of Newhouse regions in a neighborhood of systems with a structurally unstable homoclinic Poincaré curve (the multidimensional case)”, Dokl. Akad. Nauk, 329:4 (1993), 404–407; Dokl. Math., 47:2 (1993), 268–273

Citation in format AMSBIB
\Bibitem{GonTurShi93}
\by S.~V.~Gonchenko, D.~V.~Turaev, L.~P.~Shilnikov
\paper On the existence of Newhouse regions in a neighborhood of systems
with a structurally unstable homoclinic Poincar\'e curve (the
multidimensional case)
\jour Dokl. Akad. Nauk
\yr 1993
\vol 329
\issue 4
\pages 404--407
\mathnet{http://mi.mathnet.ru/dan5235}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1238829}
\zmath{https://zbmath.org/?q=an:0823.58030}
\transl
\jour Dokl. Math.
\yr 1993
\vol 47
\issue 2
\pages 268--273


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Belykh, “Chaotic and strange attractors of a two-dimensional map”, Sb. Math., 186:3 (1995), 311–326  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. O. V. Sten'kin, L. P. Shilnikov, “Homoclinic $\Omega$-explosion and domains of hyperbolicity”, Sb. Math., 189:4 (1998), 603–622  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. V. Gonchenko, V. S. Gonchenko, “On Bifurcations of Birth of Closed Invariant Curves in the Case of Two-Dimensional Diffeomorphisms with Homoclinic Tangencies”, Proc. Steklov Inst. Math., 244 (2004), 80–105  mathnet  mathscinet  zmath
    5. E. A. Sataev, “Non-existence of stable trajectories in non-autonomous perturbations of systems of Lorenz type”, Sb. Math., 196:4 (2005), 561–594  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. 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
    7. 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
    8. Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov, “Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone”, Regul. Chaotic Dyn., 18:5 (2013), 521–538  mathnet  crossref  mathscinet  zmath
    9. S. V. Gonchenko, M. S. Gonchenko, I. O. Sinitsky, “On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles”, Izv. Math., 84:1 (2020), 23–51  mathnet  crossref  crossref  isi  elib
    10. S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov, “Three Types of Attractors and Mixed Dynamics of Nonholonomic Models of Rigid Body Motion”, Proc. Steklov Inst. Math., 308 (2020), 125–140  mathnet  crossref  crossref  isi  elib
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