03322cam  22004218i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000370013305000220017008200120019210000400020424501220024426300090036626400600037530000340043533600260046933700280049533800270052349000740055050000680062450505230069250600500121552010720126550400410233753300950237853800360247358800470250965000250255665000220258165000370260377601680264085600440280885600480285220656415RPAM20181011173145.0m      b    000 0 cr/|||||||||||181011s2018    riu     ob    000 0 eng c  a9781470448134 (online)  aLBSOR/DLCbengerdacLBSORdRPAM00aQB351b.P527 201800a5212231 aPinzari, Gabriella,d1966-eauthor.10aPerihelia reduction and global Kolmogorov tori in the planetary problem /h[electronic resource] cGabriella Pinzari.  a1809 1aProvidence, RI :bAmerican Mathematical Society,c2018.  a1 online resource (pages cm.)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aMemoirs of the American Mathematical Society, x1947-6221 ; vv. 1218  a"September 2018. Volume 255. Number 1218 (first of 7 numbers)."00tChapter 1. Background and resultstChapter 2. Kepler maps and the Perihelia reductiontChapter 3. The $\mathcal P$-map and the planetary problemtChapter 4. Global Kolmogorov tori in the planetary problemtChapter 5. ProofstAppendix A. Computing the domain of holomorphytAppendix B. Proof of Lemma 3.2tAppendix C. Checking the non-degeneracy conditiontAppendix D. Some results from perturbation theorytAppendix E. More on the geometrical structure of the $\mathcal P$-coordinates, compared to Deprit's coordinates1 aAccess is restricted to licensed institutions  a"We prove 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 (1963) in the 60s, 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, common tool of previous literature"--cProvided by publisher.  aIncludes bibliographical references.  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2018  aMode of access : World Wide Web  aDescription based on print version record. 0aCelestial mechanics. 0aPlanetary theory. 0aDifferential equations, Partial.0 iPrint version: aPinzari, Gabriella, 1966-tPerihelia reduction and global Kolmogorov tori in the planetary problem /w(DLC)   2018040533x0065-9266z97814704410294 3Contentsuhttp://www.ams.org/memo/1218/4 3Contentsuhttps://doi.org/10.1090/memo/1218