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., 1998, Volume 3, Issue 4,Pages <nobr>3

This article is cited 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

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.

MSC: 58F36

Received: 20.11.1998

Language: English

DOI: 10.1070/RD1998v003n04ABEH000089