Add to ORKGThe planetary N-body problem. Arnold's statement on the existence of maximal tori for the planetary problem (1963). Classical Hamiltonian description (Delaunay, Poincare'). Degeneracies. A brief history of the proof of Arnold's theorem. A new approach to the planetary NBP (2011): Deprit's variables and Pinzari's regularization (the RPS variables). Torsion. Full proof of Arnold's theorem (sketch). Some consequences (measure estimates, Conley-Zehnder periodic orbits, Birkhoff normal forms)
Birkhoff normal forms for the (secular) planetary problem are investigated. Existence and uniqueness...
In 2004 J. Féjoz [Démonstration du ‘théorème d’Arnold’ sur la stabilité du système planétaire (d’ap...
Abstract. For any N ≥ 2 we prove the existence of quasi-periodic orbits lying on N-dimensional invar...
Arnold's theorem on the planetary problem states that, assuming that the masses of n planets are sma...
The closure of periodic orbits in the phase space of the spatial, planetary N–body problem (with wel...
The 6n-dimensional phase space of the planetary (1 + n)-body problem (after the classical reduction...
We review analytical (rigorous) results about the existence of invariant tori for planetary many-bo...
International audienceWe present a new set of variables for the reduction of the planetary n-body pr...
We introduce the $N$-body problem of mathematical celestial mechanics, and discuss its astronomical ...
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type ...
The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group an...
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type ...
In the first two lectures, hamiltonian techniques are applied to avatars of the N-body problem of in...
This third edition text provides expanded material on the restricted three body problem and celestia...
We prove the existence of an almost full measure set of (3n - 2)-dimensional quasi-periodic motions ...
Birkhoff normal forms for the (secular) planetary problem are investigated. Existence and uniqueness...
In 2004 J. Féjoz [Démonstration du ‘théorème d’Arnold’ sur la stabilité du système planétaire (d’ap...
Abstract. For any N ≥ 2 we prove the existence of quasi-periodic orbits lying on N-dimensional invar...
Arnold's theorem on the planetary problem states that, assuming that the masses of n planets are sma...
The closure of periodic orbits in the phase space of the spatial, planetary N–body problem (with wel...
The 6n-dimensional phase space of the planetary (1 + n)-body problem (after the classical reduction...
We review analytical (rigorous) results about the existence of invariant tori for planetary many-bo...
International audienceWe present a new set of variables for the reduction of the planetary n-body pr...
We introduce the $N$-body problem of mathematical celestial mechanics, and discuss its astronomical ...
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type ...
The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group an...
We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type ...
In the first two lectures, hamiltonian techniques are applied to avatars of the N-body problem of in...
This third edition text provides expanded material on the restricted three body problem and celestia...
We prove the existence of an almost full measure set of (3n - 2)-dimensional quasi-periodic motions ...
Birkhoff normal forms for the (secular) planetary problem are investigated. Existence and uniqueness...
In 2004 J. Féjoz [Démonstration du ‘théorème d’Arnold’ sur la stabilité du système planétaire (d’ap...
Abstract. For any N ≥ 2 we prove the existence of quasi-periodic orbits lying on N-dimensional invar...