Hausdorff dimension of oscillatory motions for the 3-body problem

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• Vadim Kaloshin, Penn. State
• Wednesday 25 May 2011, 16:00-17:00
• MR13.

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Consider the classical 3-body problem, where the 3 bodies are mutually attracted by Newton gravitation. Call the motions oscillatory if as time tends to infinity, limsup of maximal distance among the bodies is infinite, but the 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. This is a joint work with Anton Gorodetski.

This talk is part of the Differential Geometry and Topology Seminar series.

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