<abstract xmlns="http://www.w3.org/1999/xhtml">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<disp-formula id="j_AMNS.2018.2.00041_eq_001_w2aab3b7d630b1b6b1aab1c14b2aAa"><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mstyle><mi>H</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></munderover><msubsup><mi>p</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mi>V</mi><mo>(</mo><msub><mi>q</mi><mn>1</mn></msub><mo>,</mo><msub><mi>q</mi><mn>2</mn></msub><mo>)</mo><mo>,</mo></mstyle></mtd></mtr></mtable></math><tex-math>$$\begin{array}{}
\displaystyle H=\frac{1}{2}\sum_{i=1}^{2}p_i^2+V(q_1,q_2),
\end{array} $$</tex-math></alternatives></disp-formula>where <italic>V</italic>(<italic>q</italic>1,<italic>q</italic>2) are homogeneous polynomial potentials of degree <italic>k</italic>.</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 formH=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.

On the integrability of the Hamiltonian systems with homogeneous polynomial potentials

School of Mathematical Sciences, MOE–LSC

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

On the integrability of the Hamiltonian systems with homogeneous polynomial potentials

Published Online: Dec 31, 2018

Page range: 527 - 536

Received: Sep 24, 2018

Accepted: Dec 24, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00041

Keywords
Hamiltonian system with 2–degrees of freedom, homogeneous polynomial potential, integrability

© 2018 J. Llibre and X. Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the integrability of the Hamiltonian systems with homogeneous polynomial potentials

Published Online: Dec 31, 2018

Page range: 527 - 536

Received: Sep 24, 2018

Accepted: Dec 24, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00041

KeywordsHamiltonian system with 2–degrees of freedom, homogeneous polynomial potential, integrability

© 2018 J. Llibre and X. Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hamiltonian system with 2–degrees of freedom, homogeneous polynomial potential, integrability