ON THE MEROMORPHIC NON-INTEGRABILITY OF SOME N-BODY PROBLEMS

被引：16

作者：

Morales-Ruiz, Juan J. ^{[1
]}

Simon, Sergi ^{[2
]}

机构：

[1] Univ Politecn Madrid, Ingn Civil ETSI Caminos, Dept Matemat & Informat Aplicadas, E-28040 Madrid, Spain

[2] Univ Limoges, XLIM UMR CNRS 6172, Dept Math Informat, F-87060 Limoges, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2009年 / 24卷 / 04期

关键词：

Obstructions to integrability (nonintegrability criteria) in Hamiltonian systems; differential algebra; Dynamical systems in classical and celestial mechanics; N-body problems; REGULAR POLYGON SOLUTIONS; RELATIVE EQUILIBRIUM; INTEGRAL MANIFOLDS; SIMPLER PROOF; NONEXISTENCE; OPERATORS; THEOREM;

D O I：

10.3934/dcds.2009.24.1225

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1225 / 1273

页数：49

共 50 条

[1] The meromorphic non-integrability of the three-body problem
Tsygvintsev, A
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2001, 537 : 127 - 149
[2] The meromorphic non-integrability of the planar three-body problem
Tsygvintsev, A
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (03): : 241 - 244
[3] Non-integrability of some few body problems in two degrees of freedom
Acosta-Humánez P.B.
Álvarez-Ramírez M.
Delgado J.
[J]. Qualitative Theory of Dynamical Systems, 2009, 8 (2) : 209 - 239
[4] Non-integrability of the equal mass n-body problem with non-zero angular momentum
Combot, Thierry
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2012, 114 (04): : 319 - 340
[5] Non-integrability of the equal mass n-body problem with non-zero angular momentum
Thierry Combot
[J]. Celestial Mechanics and Dynamical Astronomy, 2012, 114 : 319 - 340
[6] A new non-integrability criterion for a meromorphic Hamiltonian
Tosel, EJ
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (12): : 1097 - 1102
[7] Meromorphic parametric non-integrability; the inverse square potential
Tosel, EJ
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2000, 152 (03) : 187 - 205
[8] Meromorphic Parametric Non-Integrability;¶the Inverse Square Potential
Emmanuelle Julliard Tosel
[J]. Archive for Rational Mechanics and Analysis, 2000, 152 : 187 - 205
[9] Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group
Stachowiak, Tomasz
Maciejewski, Andrzej J.
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2021, 17
[10] Meromorphic non-integrability of a steady Stokes flow inside a sphere
Nishiyama, Takahiro
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2014, 34 : 616 - 627

← 1 2 3 4 5 →