Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result

Gabriella Pinzari

doi:10.3934/era.2015.22.55

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2015, Volume 22: 55-75. Doi: 10.3934/era.2015.22.55 open access

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Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result

Gabriella Pinzari^1,

1.
Dipartimento di Matematica ed Applicazioni "R. Caccioppoli”, Università di Napoli "Federico II”, Monte Sant’Angelo – Via Cinthia I-80126 Napoli

Received: May 31, 2014

Revised: January 31, 2015

Published: January 2015

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Abstract

We improve a result in [9] by proving the existence of a positive measure set of $(3n-2)$-dimensional quasi-periodic motions in the spacial, planetary $(1+n)$-body problem away from co-planar, circular motions. We also prove that such quasi-periodic motions reach with continuity corresponding $(2n-1)$-dimensional ones of the planar problem, once the mutual inclinations go to zero (this is related to a speculation in [2]). The main tool is a full reduction of the SO(3)-symmetry, which retains symmetry by reflections and highlights a quasi-integrable structure, with a small remainder, independently of eccentricities and inclinations.

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Mathematics Subject Classification: 34D10, 34C20, 70E55, 70F10, 70F15, 70F07, 37J10, 37J15, 37J25, 37J35, 37J40, 70K45.

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