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| In 1963 V. A. Arnold stated that, in the planetary problem, a positive measure set of bounded motions may be found, provided the masses of the planets, eccentricities and inclinations are sufficiently small. The complete proof of this statement took more than fifty years to come to the light. After the first proof given by M. Herman and J. F\'ejoz, the theorem was directly (and quantitatively) reproved in 2011 by L. Chierchia and myself. In particular, we proved that the ``density'' of bounded motions tends to one as soon as eccentricities and inclinations go to zero. In this talk, we shall discuss the possibility of rendering this density independent of eccentricities. |
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