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Conference: Symposium on Mathematical Physics


Global Kolmogorov tori in the planetary problem

Dr. Gabriella Pinzari's talk
Date: 11.11.14   Time: 11.15 - 12.15   Room: Y27H28

We shall talk about 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's limit value and relatively high inclinations. This extends previous results in [Arnold, 1963], [Robutel, 1995], [F\'ejoz, 2004], [P. PhD, 2009], [Chierchia-P., 2011] where smallness of eccentricities and inclinations was assumed. 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. This allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, common tool of previous literature.