### 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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