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Perihelia reduction and global Kolmogorov tori in the planetary problem / Gabriella Pinzari.

By: Pinzari, Gabriella, 1966- [author.].
Material type: TextTextSeries: Memoirs of the American Mathematical Society, Volume 255, number 1218.Publisher: Providence, RI, USA : American Mathematical Society, [2018] Copyright date: ©2018Description: v, 92 pages ; 26 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470441029; 1470441020.Subject(s): Celestial mechanics | Planetary theory | Differential equations, PartialDDC classification: 521
Contents:
Background and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs.
Summary: "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"-- Provided by publisher.
List(s) this item appears in: 2019-07-26
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		515.353 PIN (Browse shelf) Available 10686
Total holds: 0

"September 2018. Volume 255. Number 1218 (first of 7 numbers)."

Includes bibliographical references (pages 91-92).

Background and results -- Kepler maps and the Perihelia reduction -- The P-map 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 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"-- Provided by publisher.