Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))

Date:	2022
Abstract:	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.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Hamiltonian system with 2-degrees of freedom ; Homogeneous potential of degree -4 ; Meromorphic integrability ; Darboux point
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 27, Núm. 8 (August 2022) , p. 4305-4316, ISSN 1553-524X

DOI: 10.3934/dcdsb.2021228

Postprint 11 p, 404.9 KB

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