学术活动
Non-avoided crossings for n-body balanced configurations in R^3 near a central configuration
2015-01-13
来源：科技处 供稿：冀俊宇 点击次数：
主讲人：Prof. Alain CHENCINER（巴黎七大，巴黎天文台）
时间：1月13日（周二）15:00-16:30
地点：必赢76net线路官网北一区文科楼 707 教室
摘要：The balanced configurations are those n-body configurations which admit a relative equilibrium motion in a Euclidean space E of high enough dimension 2p. They are characterized by the commutation of two symmetric endomorphisms of the (n-1)-dimensional Euclidean space of codispositions, the intrinsic inertia endomorphism B which encodes the shape and the Wintner-Conley endomorphism A which encodes the forces. In general, p is the dimension d of the configuration, which is also the rank of B. Lowering to 2(d-1) the dimension of E occurs when the restriction of A to the (invariant) image of B possesses a double eigenvalue. It is shown that, while in the space of all dxd-symmetric endomorphisms, having a double eigenvalue is a condition of codimension 2 (the avoided crossings of physicists), here it becomes of codimension 1. This implies in particular the existence, in the neighborhood of the regular tetrahedron configuration of 4 bodies with no three of the masses equal, of exactly 3 families of balanced configurations which admit relative equilibrium motion in a four dimensional space.
时间：1月13日（周二）15:00-16:30
地点：必赢76net线路官网北一区文科楼 707 教室
摘要：The balanced configurations are those n-body configurations which admit a relative equilibrium motion in a Euclidean space E of high enough dimension 2p. They are characterized by the commutation of two symmetric endomorphisms of the (n-1)-dimensional Euclidean space of codispositions, the intrinsic inertia endomorphism B which encodes the shape and the Wintner-Conley endomorphism A which encodes the forces. In general, p is the dimension d of the configuration, which is also the rank of B. Lowering to 2(d-1) the dimension of E occurs when the restriction of A to the (invariant) image of B possesses a double eigenvalue. It is shown that, while in the space of all dxd-symmetric endomorphisms, having a double eigenvalue is a condition of codimension 2 (the avoided crossings of physicists), here it becomes of codimension 1. This implies in particular the existence, in the neighborhood of the regular tetrahedron configuration of 4 bodies with no three of the masses equal, of exactly 3 families of balanced configurations which admit relative equilibrium motion in a four dimensional space.
