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Analytic Lagrangian tori for the planetary many-body problem. (English) Zbl 1173.37067
The planetary many-body problem consists of studying the evolution of \((n+1)\) bodies (point masses), subject only to mutual gravitation attraction, in the case where one of the bodies (the ‘Sun’) has a mass considerably larger than the masses of the remaining \(n\) bodies (the ‘planets’). The invariant tori associated with the motions provided by the well-known Arnold Theorem, in view of KAM tools, are smooth. Now, since the many-body problem is formulated in terms of real-analytic functions, it appears somewhat more natural to seek for real-analytic invariant manifolds. This is the problem addressed in this paper and, in particular, a new proof of Arnold’s statement is obtained.

MSC:
37N05 Dynamical systems in classical and celestial mechanics
70F10 \(n\)-body problems
70F15 Celestial mechanics
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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