visitant ::
identificació
|
|||||||||||||||
Cerca | Lliura | Ajuda | Servei de Biblioteques | Sobre el DDD | Català English Español |
Pàgina inicial > Articles > Articles publicats > Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4 |
Data: | 2021 |
Resum: | 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. |
Ajuts: | Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Hamiltonian system with 2-degrees of freedom ; Homogeneous potential of degree −4 ; Meromorphic integrability ; Darboux point |
Publicat a: | Discrete and continuous dynamical systems. Series B, 2021 , ISSN 1553-524X |
Postprint 11 p, 404.9 KB |