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 SIGMA, 2013, Volume 9, 059, 18 pages (Mi sigma842)

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

Oksana Bihuna, Francesco Calogerob

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

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 $t\rightarrow \infty$.

Keywords: many-body problems; $N$-body problems; partial differential equations; isochronous systems.

DOI: https://doi.org/10.3842/SIGMA.2013.059

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ArXiv: 1310.2335
MSC: 70F10; 70H06; 37J35; 37K10
Received: June 7, 2013; in final form October 2, 2013; Published online October 9, 2013
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Citation: Oksana Bihun, Francesco Calogero, “Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces”, SIGMA, 9 (2013), 059, 18 pp.

Citation in format AMSBIB
\Bibitem{BihCal13} \by Oksana~Bihun, Francesco~Calogero \paper Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces \jour SIGMA \yr 2013 \vol 9 \papernumber 059 \totalpages 18 \mathnet{http://mi.mathnet.ru/sigma842} \crossref{https://doi.org/10.3842/SIGMA.2013.059} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3116194} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325390000001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84885612962} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bihun O., Calogero F., “Equilibria of a Solvable N-Body Problem and Related Properties of the N Numbers X(N) at Which the Jacobi Polynomial of Order N Has the Same Value”, J. Nonlinear Math. Phys., 20:4 (2013), 539–551
2. Bihun O., Calogero F., “Properties of the Zeros of Generalized Hypergeometric Polynomials”, J. Math. Anal. Appl., 419:2 (2014), 1076–1094
3. Calogero F., “Three New Classes of Solvable N-Body Problems of Goldfish Type with Many Arbitrary Coupling Constants”, Symmetry-Basel, 8:7 (2016), 53
4. Calogero F., “New solvable dynamical systems”, J. Nonlinear Math. Phys., 23:4 (2016), 486–493
5. Calogero F., “A Solvable $N$-body Problem of Goldfish Type Featuring $N^2$ Arbitrary Coupling Constants”, J. Nonlinear Math. Phys., 23:2 (2016), 300–305
6. Bihun O., Calogero F., “A new solvable many-body problem of Goldfish type”, J. Nonlinear Math. Phys., 23:1 (2016), 28–46
7. F. Calogero, “Yet another class of new solvable n-body problems of goldfish type”, Qual. Theor. Dyn. Syst., 16:3 (2017), 561–577
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