02963nam 2200529 450 991047889230332120210901203040.01-4704-4813-0(CKB)4100000007133847(MiAaPQ)EBC5571100(PPN)231945795(Au-PeEL)EBL5571100(OCoLC)1042567345(EXLCZ)99410000000713384720181204d2018 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierPerihelia reduction and global Kolmogorov tori in the planetary problem /Gabriella PinzariProvidence, Rhode Island :American Mathematical Society,[2018]©20181 online resource (104 pages)Memoirs of the American Mathematical Society ;Volume 255, Number 1218"September 2018. Volume 255. Number 1218 (first of 7 numbers)."1-4704-4102-0 Includes bibliographical references.Background and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs.The author proves the existence of an almost full measure set of (3n-2)-dimensional quasi-periodic motions in the planetary problem with (1+n) masses, with eccentricities arbitrarily close to the Levi-Civita 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 in the 1960s, for the particular case of the planar three-body 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, a common tool of previous literature.Memoirs of the American Mathematical Society ;Volume 255, Number 1218.0065-9266Celestial mechanicsDifferential equations, PartialPlanetary theoryElectronic books.Celestial mechanics.Differential equations, Partial.Planetary theory.521Pinzari Gabriella1966-1054602MiAaPQMiAaPQMiAaPQBOOK9910478892303321Perihelia reduction and global Kolmogorov tori in the planetary problem2487374UNINA