Article
On the integrability of the Hamiltonian systems with homogeneous polynomial potentials
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Abstract
We summarize the known results on the integrability of the complex Hamiltonian systems with two degrees of freedom defined by the Hamiltonian functions of the form
H=12∑i=12pi2+V(q1,q2),
$$\begin{array}{}
\displaystyle H=\frac{1}{2}\sum_{i=1}^{2}p_i^2+V(q_1,q_2),
\end{array} $$
where V(q1,q2) are homogeneous polynomial potentials of degree k.
Keywords
Hamiltonian system with 2–degrees of freedom, homogeneous polynomial potential, integrability, 37J35
Citation
Llibre, J. & Zhang, X. (2018). On the integrability of the hamiltonian systems with homogeneous polynomial potentials. Applied Mathematics and Nonlinear Sciences, 3(2), 527–536. https://doi.org/10.2478/AMNS.2018.2.00041
J. Llibre and X. Zhang, “On the integrability of the hamiltonian systems with homogeneous polynomial potentials,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, pp. 527–536, 2018, doi: 10.2478/AMNS.2018.2.00041.
Llibre J, Zhang X. On the integrability of the hamiltonian systems with homogeneous polynomial potentials. Applied Mathematics and Nonlinear Sciences. 2018;3(2):527–536. doi:10.2478/AMNS.2018.2.00041.
Llibre, J. and Zhang, X. (2018), ‘On the integrability of the hamiltonian systems with homogeneous polynomial potentials’, Applied Mathematics and Nonlinear Sciences, 3(2), pp. 527–536. Available at: https://doi.org/10.2478/AMNS.2018.2.00041.
Llibre, Jaume, and Xiang Zhang. “On the Integrability of the Hamiltonian Systems with Homogeneous Polynomial Potentials.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, 2018, pp. 527–536. https://doi.org/10.2478/AMNS.2018.2.00041.
Llibre, Jaume, and Xiang Zhang. “On the Integrability of the Hamiltonian Systems with Homogeneous Polynomial Potentials.” Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 527–536. https://doi.org/10.2478/AMNS.2018.2.00041.
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Published by: Engineering Journals
