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”, Trudy Mat. Inst. Steklova, 2004, Volume 244,Pages <nobr>115

This article is cited in 8 papers

Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency

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

^a Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
^b Weierstrass Institute for Applied Analysis and Stochastics

Abstract: We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.

UDC: 517.91+517.93

Received in November 2001