
SIGMA 9 (2013), 059, 18 pages arXiv:1310.2335
http://dx.doi.org/10.3842/SIGMA.2013.059
Solvable ManyBody Models of Goldfish Type with One, Two and ThreeBody Forces
Oksana Bihun ^{a} and Francesco Calogero ^{b}
^{a)} Department of Mathematics, Concordia College at Moorhead, MN, USA
^{b)} Physics Department, University of Rome ''La Sapienza'', Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy
Received June 07, 2013, in final form October 02, 2013; Published online October 09, 2013
Abstract
The class of solvable manybody problems ''of goldfish type'' is extended by including
(the additional presence of) threebody forces.
The solvable Nbody 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→ ∞.
Key words:
manybody problems; Nbody problems; partial differential equations; isochronous systems.
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