On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom

DOI10.1016/j.geomphys.2011.12.017zbMath1246.37076OpenAlexW1991822606MaRDI QIDQ413679

Jaume Llibre, Luis Fernando Mello

Publication date: 7 May 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2011.12.017

zbMATH Keywords

periodic orbitHamiltonian systemaveraging theoryHooke potential

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Averaging method for ordinary differential equations (34C29) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

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Cites Work

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• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
• Periodic solutions of nonlinear periodic differential systems with a small parameter
• Limit cycles bifurcating from a \(k\)-dimensional isochronous center contained in \(\mathbb R^n\) with \(k\leqslant n\)
• Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
• On the periodic orbits of Hamiltonian systems
• Averaging methods in nonlinear dynamical systems

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