Geodesic
Armbruster – Guckenheimer – Kim Hamiltonian System
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 1, pp. 59-76

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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. 
@article{ND_2021_17_1_a5,
     author = {M. Alvarez-Ram{\'\i}rez and A. Garc{\'\i}a and J. Vidarte},
     title = {Armbruster {\textendash} {Guckenheimer} {\textendash} {Kim} {Hamiltonian} {System}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {59--76},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_1_a5/}
}
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M. Alvarez-Ramírez; A. García; J. Vidarte. Armbruster – Guckenheimer – Kim Hamiltonian System. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 1, pp. 59-76. http://geodesic.mathdoc.fr/item/ND_2021_17_1_a5/