Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4
We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian H=(p21+p22)/2+1/P(q1,q2), being P(q1,q2) a homogeneous polynomial of degree 4 of one of the following forms ±q41, 4q31q2, ±6q21q22, ±(q21+q22)2, ±q22(6q21-q22), ±q22(6q21+q22), q41+6μq21q22-q42, -q41+...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:258583 |
| Acceso en línea: | https://ddd.uab.cat/record/258583 https://dx.doi.org/urn:doi:10.3934/dcdsb.2021228 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian system with 2-degrees of freedom Homogeneous potential of degree -4 Meromorphic integrability Darboux point |
| Sumario: | We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian H=(p21+p22)/2+1/P(q1,q2), being P(q1,q2) a homogeneous polynomial of degree 4 of one of the following forms ±q41, 4q31q2, ±6q21q22, ±(q21+q22)2, ±q22(6q21-q22), ±q22(6q21+q22), q41+6μq21q22-q42, -q41+6μq21q22+q42 with μ>-1/3 and μ≠1/3, and q41+6μq21q22+q42 with μ≠±1/3. We note that any homogeneous polynomial of degree 4 after a linear change of variables and a rescaling can be written as one of the previous polynomials. We remark that for the polynomial q41+6μq21q22+q42 when μ∈{-5/3,-2/3} we only can prove that it has no a polynomial first integral. |
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