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Russian Journal of Nonlinear Dynamics, 2021, Volume 17, Number 1, Pages 59–76
DOI: https://doi.org/10.20537/nd210106 (Mi nd742) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical problems of nonlinearity

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

M. Alvarez-Ramíreza, A. Garcíaa, J. Vidarteb

a Departamento de Matemáticas, UAM–Iztapalapa, 09340 Iztapalapa, Ciudad de México, México
b Departamento de Matemática y Física Aplicadas Universidad Católica de la Santísima Concepción, Casilla 297, Concepción, Chile
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DOI: https://doi.org/10.20537/nd210106
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.
Funding agency Grant number
Universidad Autónoma Metropolitana I5-2019
PRODEP 511-6/18-5782
M.Alvarez-Ramírez and A.García are partially supported by Programa Especial de Apoyo a la Investigación (UAM) grant number I5-2019. Jhon Edder Vidarte Olivera was supported by a PRODEP postdoc grant 511-6/18-5782, Mexico.
Received: 07.07.2020
Accepted: 17.03.2021
Bibliographic databases:
Document Type: Article
MSC: 70H33, 37J40, 85A05
Language: english
Citation: M. Alvarez-Ramírez, A. García, J. Vidarte, “Armbruster – Guckenheimer – Kim Hamiltonian System in 1:1 Resonance”, Rus. J. Nonlin. Dyn., 17:1 (2021), 59–76
Citation in format AMSBIB
\Bibitem{AlvGarVid21}
\by M.~Alvarez-Ram{\'\i}rez, A.~Garc{\'\i}a, J.~Vidarte
\paper Armbruster – Guckenheimer – Kim Hamiltonian System
in 1:1 Resonance
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 1
\pages 59--76
\mathnet{http://mi.mathnet.ru/nd742}
\crossref{https://doi.org/10.20537/nd210106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4240818}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85105152531}
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    • This publication is cited in the following 1 articles:
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