S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev, “Elliptic Periodic Orbits Near a Homoclinic Tangency in Four-Dimensional Symplectic Maps and Hamiltonian Systems With Three Degrees of Freedom”, Regul. Chaotic Dyn., 3:4 (1998), 3

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Regular and Chaotic Dynamics, 1998, Volume 3, Issue 4, Pages 3–26
DOI: https://doi.org/10.1070/RD1998v003n04ABEH000089 (Mi rcd957)

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

Elliptic Periodic Orbits Near a Homoclinic Tangency in Four-Dimensional Symplectic Maps and Hamiltonian Systems With Three Degrees of Freedom

S. V. Gonchenko^a, L. P. Shilnikov^a, D. V. Turaev^b

^a Institute for Applied mathematics and Cybernetics, 10 Ul'ianov Str., Nizhniy Novgorod, 603005, Russia
^b Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, D-10117, Berlin

Citations (10)

DOI: https://doi.org/10.1070/RD1998v003n04ABEH000089

Abstract: We study bifurcations leading to the appearance of elliptic orbits in the case of four-dimensional symplectic diffeomorphisms (and Hamiltonian flows with three degrees of freedom) with a homoclinic tangency to a saddle-focus periodic orbit.

Received: 20.11.1998

Bibliographic databases:

Document Type: Article

MSC: 58F36

Language: English

Citation: S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev, “Elliptic Periodic Orbits Near a Homoclinic Tangency in Four-Dimensional Symplectic Maps and Hamiltonian Systems With Three Degrees of Freedom”, Regul. Chaotic Dyn., 3:4 (1998), 3–26

Citation in format AMSBIB

\Bibitem{GonShiTur98}

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

\paper Elliptic Periodic Orbits Near a Homoclinic Tangency in Four-Dimensional Symplectic Maps and Hamiltonian Systems With Three Degrees of Freedom

\jour Regul. Chaotic Dyn.

\yr 1998

\vol 3

\issue 4

\pages 3--26

\mathnet{http://mi.mathnet.ru/rcd957}

\crossref{https://doi.org/10.1070/RD1998v003n04ABEH000089}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1704979}

\zmath{https://zbmath.org/?q=an:0956.37048}

Linking options:

https://www.mathnet.ru/eng/rcd957

https://www.mathnet.ru/eng/rcd/v3/i4/p3

This publication is cited in the following 10 articles:

Amadeu Delshams, Marina Gonchenko, Sergey Gonchenko, “On dynamics and bifurcations of area-preserving maps with homoclinic tangencies”, Nonlinearity, 28:9 (2015), 3027
Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko, “On Bifurcations of Area-preserving and Nonorientable Maps with Quadratic Homoclinic Tangencies”, Regul. Chaotic Dyn., 19:6 (2014), 702–717
S.V. Gonchenko, A.S. Gonchenko, I.I. Ovsyannikov, D.V. Turaev, L. Lerman, D. Turaev, V. Vougalter, M. Zaks, “Examples of Lorenz-like Attractors in Hénon-like Maps”, Math. Model. Nat. Phenom., 8:5 (2013), 48
S. V. Gonchenko, V. S. Gonchenko, L. P. Shilnikov, “On a homoclinic origin of Hénon-like maps”, Regul. Chaotic Dyn., 15:4 (2010), 462–481
M. S. Gonchenko, S. V. Gonchenko, “On Cascades of Elliptic Periodic Points in Two-Dimensional Symplectic Maps with Homoclinic Tangencies”, Regul. Chaotic Dyn., 14:1 (2009), 116–136
A. Rapoport, V. Rom-Kedar, D. Turaev, “Stability in High Dimensional Steep Repelling Potentials”, Commun. Math. Phys., 279:2 (2008), 497
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
Jeroen S W Lamb, Oleg V Stenkin, “Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits”, Nonlinearity, 17:4 (2004), 1217
V. S. Gonchenko, “Homoclinic Tangencies, $\Omega$ -Moduli, and Bifurcations”, Proc. Steklov Inst. Math., 236 (2002), 94–109
S. V. Gonchenko, L. P. Shilnikov, “Hyperbolic properties of four-dimensional symplectic mappings with a structurally unstable trajectory homoclinic to a fixed point of the saddle-focus type”, Differ. Equ., 36:11 (2000), 1610–1620

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

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