Record:   Prev Next
作者 Pinzari, Gabriella. Author.
書名 Perihelia reduction and global Kolmogorov tori in the planetary problem / Gabriella Pinzari
出版項 Providence, Rhode Island : AMS, American Mathematical Society
copyright 2018
國際標準書號 9781470441029 (br)
1470441020 (br)
國際標準號碼 9781470441029
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QB351 P527 2018    在架上    30340200561227
說明 1 vol. (V-92 p.) ; 26 cm
系列 Memoirs of the American Mathematical Society, 0065-9266 ; 1218
Memoirs of the American Mathematical Society ; 1218. 0065-9266
附註 Bibliogr. p. 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
主題 Celestial mechanics
Differential equations, Partial
Planetary theory
Record:   Prev Next