Perihelia reduction and Global Kolmogorov tori in the planetary problem /

"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 small...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Pinzari, Gabriella, 1966- (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, Rhode Island : American Mathematical Society, [2018]
Series:Memoirs of the American Mathematical Society ; no. 1218.
Subjects:
Celestial mechanics.
Planetary theory.
Differential equations, Partial.
Mécanique céleste.
Théorie des planètes.
Équations aux dérivées partielles.
SCIENCE > Astronomy.
Mecánica celeste
Ecuaciones diferenciales
Celestial mechanics
Differential equations, Partial
Planetary theory
Online Access:Texto completo
Table of 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
  • Appendix A. Computing the domain of holomorphy
  • Appendix B. Proof of Lemma 3.2
  • Appendix C. Checking the non-degeneracy condition
  • Appendix D. Some results from perturbation theory
  • Appendix E. More on the geometrical structure of the P-coordinates, compared to Deprit's coordinates.

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