Hausdorff dimension of oscillatory motions for the 3-body problem
Vadim Kaloshin (Maryland)

Consider the classical 3-body problem mutually attracted by Newton
gravitation. Call motions oscillatory if at time tends to infinity limsup
of maximal distance among the bodies is infinite, while liminf is
finite. In the '50s Sitnikov presented the first rigorous example of
oscillatory motions for the so-called restricted 3-body problem. Later in
the '60s Alexeev extended this example to the 3-body problem. A
long-standing conjecture, probably going back to 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 have full Hausdorff dimension.

Colloquium, Department of Mathematics, Rice University
November 29, 2007 4:00-5:00 PM, HB 227

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