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020 a| 9781470441029q| (pbk. : alk. paper);

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100 1 a| Pinzari, Gabriella,d| 1966-?| UNAUTHORIZED;

245 10 a| Perihelia reduction and global Kolmogorov tori in the planetary problemh| [electronic resource] /c| Gabriella Pinzari.;

260 a| Providence, RI, USA :b| American Mathematical Society, [2018];

300 a| v, 92 pages ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 255, number 1218;

500 a| "September 2018. Volume 255. Number 1218 (first of 7 numbers).";

504 a| Includes bibliographical references (pages 91-92).;

505 0 a| Background and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Celestial mechanics.=| ^A72247;

650 0 a| Planetary theory.=| ^A48381;

650 0 a| Differential equations, Partial.=| ^A20205;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=5571100;

856 40 z| Full text available from Memoirs of the American Mathematical Societyu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.ams.org%2Fmemo%2F1218%2F;

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

Author/creator	Pinzari, Gabriella, 1966-
Format	Electronic
Publication Info	Providence, RI, USA : American Mathematical Society, [2018]
Description	v, 92 pages ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Supplemental Content	Full text available from Memoirs of the American Mathematical Society
Subjects	Celestial mechanics. Planetary theory. Differential equations, Partial.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 255, number 1218
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.
Abstract	"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.
General note	"September 2018. Volume 255. Number 1218 (first of 7 numbers)."
Bibliography note	Includes bibliographical references (pages 91-92).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2018040533
ISBN	9781470441029 (pbk. : alk. paper)
ISBN	1470441020 (pbk. : alk. paper)

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

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