On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n
We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1/2 d∑i=1 p21+V(q1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221335 |
| Acesso em linha: | https://ddd.uab.cat/record/221335 https://dx.doi.org/urn:doi:10.1142/S0219199717500456 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hamiltonian systems Weight-homogenous differential systems Polynomial integrability Darboux polynomials Exponential factors Darboux first integrals |
| Resumo: | We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1/2 d∑i=1 p21+V(q1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral. |
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