LEADER 02963nam 2200529 450 001 9910478892303321 005 20210901203040.0 010 $a1-4704-4813-0 035 $a(CKB)4100000007133847 035 $a(MiAaPQ)EBC5571100 035 $a(PPN)231945795 035 $a(Au-PeEL)EBL5571100 035 $a(OCoLC)1042567345 035 $a(EXLCZ)994100000007133847 100 $a20181204d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPerihelia reduction and global Kolmogorov tori in the planetary problem /$fGabriella Pinzari 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2018] 210 4$dİ2018 215 $a1 online resource (104 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 255, Number 1218 300 $a"September 2018. Volume 255. Number 1218 (first of 7 numbers)." 311 $a1-4704-4102-0 320 $aIncludes bibliographical references. 327 $aBackground and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs. 330 $aThe author proves the existence of an almost full measure set of (3n-2)-dimensional quasi-periodic motions in the planetary problem with (1+n) masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold in the 1960s, for the particular case of the planar three-body problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, a common tool of previous literature. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 255, Number 1218.$x0065-9266 606 $aCelestial mechanics 606 $aDifferential equations, Partial 606 $aPlanetary theory 608 $aElectronic books. 615 0$aCelestial mechanics. 615 0$aDifferential equations, Partial. 615 0$aPlanetary theory. 676 $a521 700 $aPinzari$b Gabriella$f1966-$01054602 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910478892303321 996 $aPerihelia reduction and global Kolmogorov tori in the planetary problem$92487374 997 $aUNINA