Periodic orbits of perturbed non-axially symmetric potentials in \(1:1:1\) and \(1:1:2\) resonances

DOI10.3934/dcdsb.2018101zbMath1403.37070OpenAlexW2791527142WikidataQ129525599 ScholiaQ129525599MaRDI QIDQ1634877

Jaume Llibre, Claudia Valls, Montserrat Corbera

Publication date: 18 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018101

zbMATH Keywords

periodic solutionslinear stabilityaveraging theorygalactic potentialgeneralized Hénon-Heiles Hamiltonian

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Averaging method for ordinary differential equations (34C29) Dynamics induced by flows and semiflows (37C10) Dynamical systems in classical and celestial mechanics (37N05)

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Cites Work

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• On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family
• Escape regions of a quartic potential
• Averaging methods for finding periodic orbits via Brouwer degree.
• On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials
• Periodic trajectories near degenerate equilibria in the Hénon-Heiles and Yang-Mills Hamiltonian systems
• Periodic orbits and non-integrability of Hénon–Heiles systems
• Formal integrals for an autonomous Hamiltonian system near an equilibrium point
• The Hénon and Heiles Problem in Three Dimensions.
• Perturbed ion traps: A generalization of the three-dimensional Hénon–Heiles problem
• A degenerate bifurcation in the Hénon-Heiles family