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- W4226518864 abstract "This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree $k$ of type $V_{k,l}=alpha (q_2-i q_1)^l (q_2+iq_1)^{k-l}$ with $alphainmathbb{C}$ and $l=0,1,dots, k$, called exceptional potentials. Hietarinta cite{Hietarinta1983} proved that the potentials with $l=0,1,k-1,k$ and $l=k/2$ for $k$ even are polynomial integrable. We present an elementary proof of this fact in the context of the polynomial bi-homogeneous potentials, as was introduced by Combot et al. cite{Combot2020}. In addition, we take advantage of the fact that we can exchange the exponents to derive an additional first integral for $V_{7,5}$, unknown so far. The paper concludes with a Galoisian analysis for $l=k/2$." @default.
- W4226518864 created "2022-05-05" @default.
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- W4226518864 date "2021-12-09" @default.
- W4226518864 modified "2023-10-18" @default.
- W4226518864 title "A note on the integrability of exceptional potentials via polynomial bi-homogeneous potentials" @default.
- W4226518864 hasPublicationYear "2021" @default.
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