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math.DS2004
Fitting Hyperbolic Pants to a Three-Body Problem
Richard Montgomery
Consider the three-body problem with an attractive potential. Modulo symmetries, the dynamics of the bounded zero-angular momentum solutions is equivalent to a geodesic flo…
math.DS2003
Convexity in the Figure Eight Solution to the Three-Body Problem
Toshiaki Fujiwara, Richard Montgomery
The figure eight is a remarkable solution to the Newtonian three-body problem in which the three equal masses chase each around a planar curve having the qualitative shape and symm…
math.DS2001
Infinitely Many Eclipses
Richard Montgomery
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suff…