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Saari's homographic conjecture of the three-body problem
Author(s):
Florin
Diacu;
Toshiaki
Fujiwara;
Ernesto
Pérez-Chavela;
Manuele
Santoprete
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6447-6473.
MSC (2000):
Primary 70F10, 70H05
Posted:
May 29, 2008
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Abstract:
Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian  -body problem with constant configurational measure are homographic. In other words, if the mutual distances satisfy a certain relationship, the configuration of the particle system may change size and position but not shape. We prove this conjecture for large sets of initial conditions in three-body problems given by homogeneous potentials, including the Newtonian one. Some of our results are true for  .
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Additional Information:
Florin
Diacu
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
Email:
diacu@math.uvic.ca
Toshiaki
Fujiwara
Affiliation:
College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 228-8555, Japan
Email:
fujiwara@clas.kitasato-u.ac.jp
Ernesto
Pérez-Chavela
Affiliation:
Departamento de Matemáticas, UAM--Iztapalapa, A.P. 55--534, 09340 Iztapalapa, Mexico, D.F., Mexico
Email:
epc@xanum.uam.mx
Manuele
Santoprete
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada
Email:
msantoprete@wlu.ca
DOI:
10.1090/S0002-9947-08-04517-0
PII:
S 0002-9947(08)04517-0
Keywords:
Three-body problem,
homographic solutions,
central configurations
Received by editor(s):
November 27, 2006
Posted:
May 29, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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