On the periodic orbits of Hamiltonian systems

DOI10.1063/1.3387343zbMath1310.70024OpenAlexW2094657444MaRDI QIDQ5249137

Jaume Llibre, Ana Rodrigues

Publication date: 29 April 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/226104

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Hamilton's equations (70H05) Averaging method for ordinary differential equations (34C29) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Orbital mechanics (70M20) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (3)

On the periodic solutions emerging from the equilibria of the Hill lunar problem with oblateness ⋮ On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom ⋮ Limit cycles for a class of second order differential equations

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
• Averaging methods in nonlinear dynamical systems

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