摘要
In our context,the planetary many-body problem consists of studying the motion of(n+1)-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the existence of real analytic lower dimensional elliptic invariant tori with intermediate dimension N lies between n and 3n-1 for the spatial planetary many-body problem.Based on a degenerate KolmogorovArnold-Moser(abbr.KAM)theorem proved by Bambusi et al.(2011),Berti and Biasco(2011),we manage to handle the difficulties caused by the degeneracy of this real analytic system.
In our context,the planetary many-body problem consists of studying the motion of（n ＋ 1）-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the existence of real analytic lower dimensional elliptic invariant tori with intermediate dimension N lies between n and 3n- 1 for the spatial planetary many-body problem.Based on a degenerate KolmogorovArnold-Moser（abbr.KAM） theorem proved by Bambusi et al.（2011）,Berti and Biasco（2011）,we manage to handle the difficulties caused by the degeneracy of this real analytic system.
