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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 journalArticlepeer-review

Harvard

Simon, S & Morales-Ruiz, J 2009, 'On the meromorphic non-integrability of some $N$-body problems', Discrete and Continuous Dynamical Systems, vol. 24, no. 4, pp. 1225-1273. https://doi.org/10.3934/dcds.2009.24.1225

APA

Simon, S., & Morales-Ruiz, J. (2009). On the meromorphic non-integrability of some $N$-body problems. Discrete and Continuous Dynamical Systems, 24(4), 1225-1273. https://doi.org/10.3934/dcds.2009.24.1225

Vancouver

Simon S, Morales-Ruiz J. On the meromorphic non-integrability of some $N$-body problems. Discrete and Continuous Dynamical Systems. 2009;24(4):1225-1273. https://doi.org/10.3934/dcds.2009.24.1225

Author

Simon, Sergi ; Morales-Ruiz, J. / On the meromorphic non-integrability of some $N$-body problems. In: Discrete and Continuous Dynamical Systems. 2009 ; Vol. 24, No. 4. pp. 1225-1273.

Bibtex

@article{54d505e3665d4cbbb1d80c31daa8a79b,
title = "On the meromorphic non-integrability of some $N$-body problems",
abstract = "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.",
author = "Sergi Simon and J. Morales-Ruiz",
year = "2009",
doi = "10.3934/dcds.2009.24.1225",
language = "English",
volume = "24",
pages = "1225--1273",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "4",

}

RIS

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