說明 
1 vol. (V92 p.) ; 26 cm 
系列 
Memoirs of the American Mathematical Society, 00659266 ; 1218


Memoirs of the American Mathematical Society ; 1218. 00659266

附註 
Bibliogr. p. 9192 

Background and results  Kepler maps and the Perihelia reduction  The Pmap and the planetary problem  Global Kolmogorov tori in the planetary problem  Proofs 

"We prove the existence of an almost full measure set of (3n  2)dimensional quasiperiodic motions in the planetary problem with (1 + n) masses, with eccentricities arbitrarily close to the LeviCivita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold (1963) in the 60s, for the particular case of the planar threebody problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, common tool of previous literature" Provided by publisher 
主題 
Celestial mechanics


Differential equations, Partial


Planetary theory

