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Perihelia reduction and global Kolmogorov tori in the planetary problem

Author: Gabriella Pinzari
Publisher: Providence, RI : AMS, American Mathematical Society, 2018.
Series: Memoirs of the American Mathematical Society, no. 1218.
Edition/Format:   Print book : EnglishView all editions and formats
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  Read more...
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Document Type: Book
All Authors / Contributors: Gabriella Pinzari
ISBN: 9781470441029 1470441020
OCLC Number: 1039596871
Notes: "September 2018. Volume 255. Number 1218 (first of 7 numbers)."
Description: v, 92 pages ; 26 cm.
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.
Series Title: Memoirs of the American Mathematical Society, no. 1218.
Responsibility: Gabriella Pinzari.

Abstract:

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  Read more...

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