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

DOI10.20537/ND210106zbMath1468.70013OpenAlexW3153440213MaRDI QIDQ4999685

Jhon Vidarte, Antonio García, Martha Alvarez-Ramírez

Publication date: 2 July 2021

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/nd742

zbMATH Keywords

periodic orbitsHamiltonian systemKAM torigalactic potentialreduced spacenormalization and reduction

Mathematics Subject Classification ID

Celestial mechanics (70F15) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Parametric resonances for nonlinear problems in mechanics (70K28)

Cites Work

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• Invariant tori in Hamiltonian systems with high order proper degeneracy
• The Lissajous transformation. I: Basics
• The Lissajous transformation. II: Normalization
• Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential
• Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem
• Differential Topology
• Singular reduction of resonant Hamiltonians
• Nonintegrability of the Armbruster--Guckenheimer--Kim Quartic Hamiltonian Through Morales--Ramis Theory
• CONNECTING SYMMETRIC AND ASYMMETRIC FAMILIES OF PERIODIC ORBITS IN SQUARED SYMMETRIC HAMILTONIANS
• Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori
• Regularization of kepler's problem and the averaging method on a manifold
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem

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