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SUMMARY:Hausdorff dimension of oscillatory motions for the 3-body problem 
 - Vadim Kaloshin\, Penn. State
DTSTART:20110525T150000Z
DTEND:20110525T160000Z
UID:TALK30171@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION: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 i
 s\ninfinite\, but the liminf is finite. In the ’50s Sitnikov presented t
 he first rigorous example of oscillatory motions for the so-called restric
 ted 3-body problem. Later in the ’60s Alexeev extended this\nexample to 
 the 3-body problem. A long-standing conjecture\, probably going back to Ko
 lmogorov\, is that oscillatory motions have measure zero. We show that for
  the Sitnikov example and for the so-called\nrestricted planar circular 3-
 body problem these motions often have full Hausdorff dimension. This is a 
 joint work with Anton Gorodetski.
LOCATION:MR13
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