
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
(3n2)dimensional quasi periodic motions in the planetary problem
with (1+n) masses, with eccentricities arbitrarily close to the
LeviCivita's limit value and relatively high inclinations. This
extends previous results in [Arnold, 1963], [Robutel, 1995], [F\'ejoz,
2004], [P. PhD, 2009], [ChierchiaP., 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.

