This article is cited in 1 paper

Mathematical problems of nonlinearity

Armbruster – Guckenheimer – Kim Hamiltonian System in 1:1 Resonance

M. Alvarez-Ramírez^a, A. García^a, J. Vidarte<sup>b

a</sup> Departamento de Matemáticas, UAM–Iztapalapa, 09340 Iztapalapa, Ciudad de México, México
^b Departamento de Matemática y Física Aplicadas Universidad Católica de la Santнsima Concepción, Casilla 297, Concepción, Chile

Abstract: This article deals with the autonomous two-degree-of-freedom Hamiltonian system with Armbruster – Guckenheimer – Kim galactic potential in 1:1 resonance depending on two parameters. We detect periodic solutions and KAM 2-tori arising from linearly stable periodic solutions not found in earlier papers. These are established by using reduction, normalization, averaging and KAM techniques.

Keywords: galactic potential, Hamiltonian system, normalization and reduction, KAM tori, reduced space, periodic orbits.

MSC: 70H33, 37J40, 85A05

Received: 07.07.2020
Accepted: 17.03.2021

Language: English

DOI: 10.20537/nd210106

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