RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 7 scientific papers (total in 7 papers)

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

Full text: PDF file (363 kB)
Full text: http://emis.mi.ras.ru/.../059
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1310.2335
MSC: 70F10; 70H06; 37J35; 37K10
Received: June 7, 2013; in final form October 2, 2013; Published online October 9, 2013
Language:

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}


Linking options:
  • http://mi.mathnet.ru/eng/sigma842
  • http://mi.mathnet.ru/eng/sigma/v9/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  crossref  mathscinet  isi  scopus
    2. Bihun O., Calogero F., “Properties of the Zeros of Generalized Hypergeometric Polynomials”, J. Math. Anal. Appl., 419:2 (2014), 1076–1094  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  isi  scopus
    4. Calogero F., “New solvable dynamical systems”, J. Nonlinear Math. Phys., 23:4 (2016), 486–493  crossref  mathscinet  isi  scopus
    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  crossref  mathscinet  isi  elib  scopus
    6. Bihun O., Calogero F., “A new solvable many-body problem of Goldfish type”, J. Nonlinear Math. Phys., 23:1 (2016), 28–46  crossref  mathscinet  isi  scopus
    7. F. Calogero, “Yet another class of new solvable n-body problems of goldfish type”, Qual. Theor. Dyn. Syst., 16:3 (2017), 561–577  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:146
    Full text:26
    References:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019