\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On the meromorphic non-integrability of some $N$-body problems

Abstract Related Papers Cited by
  • We present a proof of the meromorphic non--integrability of the planar $N$-Body Problem for some special cases. A simpler proof is added to those already existing for the Three-Body Problem with arbitrary masses. The $N$-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 $N=4,5,6$. 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.
    Mathematics Subject Classification: Primary: 37J30, 12H05; Secondary: 53C35, 37N05, 70F10.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(187) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return