Consider
the classical 3-body problem, where bodies are mutually attracted by
Newton gravitation. Call motion oscillatory if as time tends to
infinity limsup of maximal distance among the bodies is infinite, while
liminf is finite. In the 50's Sitnikov presented the first rigorous
example of ocsillatory motions for the so-called restricted 3-body
problem. Later in the 60's Alexeev extended this example to the full
3-body problem. A long-standing conjecture of Kolmogorov is that
oscillatory motions have measure zero. We show that for the Sitnikov
example and for the so-called restricted planar circular 3-body problem
these motions often form a set of maximal possible Hausdorff dimension.
