On the meromorphic non-integrability of some $N$-body problems
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On the meromorphic non-integrability of some $N$-body problems. / Simon, Sergi; Morales-Ruiz, J.
In: Discrete and Continuous Dynamical Systems, Vol. 24, No. 4, 2009, p. 1225-1273.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On the meromorphic non-integrability of some $N$-body problems
AU - Simon, Sergi
AU - Morales-Ruiz, J.
PY - 2009
Y1 - 2009
N2 - We present a proof of the meromorphic non--integrability of the planar -Body Problem for some special cases. A simpler proof is added to those already existing for the Three-Body Problem with arbitrary masses. The -Body Problem with equal masses is also proven non-integrable. Furthermore, a new general result on additional integrals is obtained which, applied to these specific cases, proves the non-existence of an additional integral for the general Three-Body Problem, and provides for an upper bound on the amount of additional integrals for the equal-mass Problem for . These results appear to qualify differential Galois theory, and especially a new incipient theory stemming from it, as an amenable setting for the detection of obstructions to Hamiltonian integrability.
AB - We present a proof of the meromorphic non--integrability of the planar -Body Problem for some special cases. A simpler proof is added to those already existing for the Three-Body Problem with arbitrary masses. The -Body Problem with equal masses is also proven non-integrable. Furthermore, a new general result on additional integrals is obtained which, applied to these specific cases, proves the non-existence of an additional integral for the general Three-Body Problem, and provides for an upper bound on the amount of additional integrals for the equal-mass Problem for . These results appear to qualify differential Galois theory, and especially a new incipient theory stemming from it, as an amenable setting for the detection of obstructions to Hamiltonian integrability.
U2 - 10.3934/dcds.2009.24.1225
DO - 10.3934/dcds.2009.24.1225
M3 - Article
VL - 24
SP - 1225
EP - 1273
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - 4
ER -
ID: 66947