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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Hausdorff dimension of oscillatory motions for the
3-body problem - Vadim Kaloshin\, Penn. State
DTSTART;TZID=Europe/London:20110525T160000
DTEND;TZID=Europe/London:20110525T170000
UID:TALK30171AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30171
DESCRIPTION:Consider the classical 3-body problem\, where the
3 bodies are mutually attracted by Newton gravitat
ion. Call the motions oscillatory if as time tends
to infinity\, limsup of maximal distance among th
e bodies is\ninfinite\, but the liminf is finite.
In the ’50s Sitnikov presented the first rigorous
example of oscillatory motions for the so-called r
estricted 3-body problem. Later in the ’60s Alexee
v extended this\nexample to the 3-body problem. A
long-standing conjecture\, probably going back to
Kolmogorov\, is that oscillatory motions have meas
ure zero. We show that for the Sitnikov example an
d for the so-called\nrestricted planar circular 3-
body problem these motions often have full Hausdor
ff dimension. This is a joint work with Anton Goro
detski.
LOCATION:MR13
CONTACT:Ivan Smith
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