scholarly journals On multiple fourth-order resonances in a nonautonomous two-degree-of-freedom Hamiltonian system

2019 ◽  
Vol 29 (2) ◽  
pp. 275-294
Author(s):  
O.V. Kholostova ◽  
Keyword(s):  
Hamiltonian System ◽  
Fourth Order ◽  
Degree Of Freedom ◽  
Two Degree Of Freedom

scholarly journals Armbruster – Guckenheimer – Kim Hamiltonian System in $\bs 1$:$\bs 1$ Resonance

2021 ◽  
Vol 17 (1) ◽  
pp. 59-76
Author(s):  
M. Alvarez-Ramírez ◽  
◽  
A. García ◽  
J. Vidarte ◽  
◽  
...  
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Degree Of Freedom ◽  
Galactic Potential ◽  
Stable Periodic ◽  
Two Parameters ◽  
Two Degree Of Freedom

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.

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