1.

Record Nr.

UNINA9910793296803321

Autore

Pinzari Gabriella <1966->

Titolo

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

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [2018]

©2018

ISBN

1-4704-4813-0

Descrizione fisica

1 online resource (104 pages)

Collana

Memoirs of the American Mathematical Society ; ; Number 1218

Disciplina

521

Soggetti

Celestial mechanics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

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

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

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

Sommario/riassunto

The 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.