Geodesic
Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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The class of solvable many-body problems “of goldfish type” is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary “coupling constants”. Restrictions on these constants are identified which cause these systems — or appropriate variants of them — to be isochronous or asymptotically isochronous, i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as $t\rightarrow \infty $.
Keywords: many-body problems; $N$-body problems; partial differential equations; isochronous systems. 
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     author = {Oksana Bihun and Francesco Calogero},
     title = {Solvable {Many-Body} {Models} of {Goldfish} {Type} with {One-,} {Two-} and {Three-Body} {Forces}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a58/}
}
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Oksana Bihun; Francesco Calogero. Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a58/

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