三体問題・N体問題

----ただいま一部閲覧可能---

三体衝突多様体
1. 直線三体問題の三体衝突
   Triple collision in the collinear three-body problem
   Richard McGehee, Invetiones Mathematicae 27(1974), 191-227
2. 平面三体問題の三体衝突
   Triple collision in the planar isosceles three body problem
   Robert L. Devaney, Inventiones Mathemticae 60(1980), 249-267
3. 平面二等辺三体問題の定性的研究
   Qualitative study of the planar isosceles three-body problem
   Carles Simo and Regina Martinez, Celestial Mechanics 41(1988), 179-251
4. 三体衝突近くのカオス力学
   Chaotic dynamics near triple collision
   Richard Moeckel, Arch. Rational Mec. 107(1989), 37-69

   N体問題の特異性

5. n体問題の特異点について
   Sur les singularites du probleme des n corps
   H. von Zeipel, Arkiv for Matematik, Astronomi och Fysik 4(1908), 1-4
6. ニュートン重力系の特異点と衝突
   Singularities and collisions of Newtonian gravitational systems
   Donald G. Saari, Arch. Rational Mech. and Anal. 49(1973), 311-320
7. 天体力学における特異性に関するvon Zeipelの定理
   Von Zeipel's theorem on singularities in celestial mechanics
   Richard McGehee, Exposiones Mathematicae 4(1986), 335-345

   振動解および非衝突特異性

8. 三体問題における振動解の存在
   The existence of oscillatory motions in the three-body problem
   K. Sitnikov, Dokl. Akad. Nauk. SSSR 133(1960), 303-306
9. 有限時間に非有界になる直線4体問題の解
   Solutions of the collinear four body problem which become unbounded in finite time
   J.N. Mather and R. Mcgehee, Lecture Notes in Physics 38(1975), 573-597
10. ニュートン系における振動運動および超双曲運動の存在
    The existence of oscillatory and super hyperbolic motions in newtonian systems
    Donald G. Saari and Zhihong Xia, Journal of Differential rquations 82(1989), 342-355
11. 制限三体問題におけるメルニコフの方法と横断的ホモクリニック点
    Melnikov method and transversal homoclinic points in the restricted three-body problem
    Zhihong Xia, Journal of Differential Equations 96(1992), 170-184
12. 平面三体問題におけるアーノルド拡散と振動解
    Arnold diffusion and oscillatory solutions in the planar three-body problem
    Zhihong Xia, Journal of Differential Equations 110(1994), 289-321
13. ニュートン系における非衝突特異性
    The existence of noncollision singularities in newtonian systems
    Zhihong Xia, Annals of Mathematics 135(1992), 411-468

    各論

14. 平面二等辺三体問題における秩序とカオス
    Order and chaos in the planar isosceles three-body problem
    K. Zare and S. Chesley, Chaos 8(1998), 475-494
    
15. 記号力学による1次元三体問題
    One-dimensional three-body problem via symbolic dynamics
    Kiyotaka Tanikawa and Seppo Mikkola, Chaos 10(2000), 649-657