M. S. Gonchenko, S. V. Gonchenko, “On Cascades of Elliptic Periodic Points in Two-Dimensional Symplectic Maps with Homoclinic Tangencies”, Regul. Chaotic Dyn., 2009, Volume 14, Issue 1,Pages <nobr>116

This article is cited in 19 papers

JÜRGEN MOSER – 80

On Cascades of Elliptic Periodic Points in Two-Dimensional Symplectic Maps with Homoclinic Tangencies

M. S. Gonchenko^a, S. V. Gonchenko^b

^a Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain
^b Research Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod State University, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia

Abstract: We study bifurcations of two-dimensional symplectic maps with quadratic homoclinic tangencies and prove results on the existence of cascade of elliptic periodic points for one and two parameter general unfoldings.

Keywords: symplectic map, homoclinic tangency, bifurcation, generic elliptic point, KAM-theory.

MSC: 37C29, 37G25, 37J10, 37J20

Received: 02.11.2008
Accepted: 21.12.2008

Language: English

DOI: 10.1134/S1560354709010080