Hausdorff dimension of oscillatory motions for the three-body problem

Series
CDSNS Colloquium
Time
Monday, September 8, 2008 - 4:30pm for 2 hours
Location
Skiles 269
Speaker
Vadim Yu Kaloshin – Mathematics Department, Penn State
Organizer
Yingfei Yi
Consider the classical Newtonian three-body problem. Call motions oscillatory if as times tends to infinity limsup of maximal distance among the bodies is infinite, while liminf it finite. In the '50s Sitnitkov gave the first rigorous example of oscillatory motions for the so-called restricted three-body problem.  Later in the '60s Alexeev extended this example to the three-body. A long-standing conjecture, probably going back to Kolmogorov, is that oscillatory motions have measure zero. We show that for the Sitnitkov example and for the so-called restricted planar circular three-body problem these motions have maximal Hausdorff dimension. This is a joint work with Anton Gorodetski.