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arXiv · 1310.2335

Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces

Oksana Bihun·Francesco Calogero
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Abstract

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 $t\rightarrow\infty$.

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Oksana Bihun, Francesco Calogero. 2013-10-09. Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces. https://doi.org/10.3842/sigma.2013.059

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