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Dokl. Akad. Nauk SSSR, 1968, Volume 180, Number 2, Pages 286–289 (Mi dan33844)  

This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus

L. P. Shilnikov

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

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Bibliographic databases:

Document Type: Article
UDC: 517.9
Presented: L. S. Pontryagin
Received: 06.07.1967

Citation: L. P. Shilnikov, “On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus”, Dokl. Akad. Nauk SSSR, 180:2 (1968), 286–289

Citation in format AMSBIB
\Bibitem{Shi68}
\by L.~P.~Shilnikov
\paper On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus
\jour Dokl. Akad. Nauk SSSR
\yr 1968
\vol 180
\issue 2
\pages 286--289
\mathnet{http://mi.mathnet.ru/dan33844}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0248861}


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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. L. P. Shilnikov, “A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type”, Math. USSR-Sb., 10:1 (1970), 91–102  mathnet  crossref  mathscinet  zmath
    2. N. K. Gavrilov, L. P. Shilnikov, “On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I”, Math. USSR-Sb., 17:4 (1972), 467–485  mathnet  crossref  mathscinet  zmath
    3. 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
    4. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency”, Proc. Steklov Inst. Math., 244 (2004), 106–131  mathnet  mathscinet  zmath
    5. 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
    6. Jacky Cresson, Stephen Wiggins, “A $\lambda$-lemma for Normally Hyperbolic Invariant Manifolds”, Regul. Chaotic Dyn., 20:1 (2015), 94–108  mathnet  crossref  mathscinet  zmath
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