English

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

Exactly Solvable and Integrable Systems 2013-10-10 v1 Dynamical Systems

Abstract

The class of solvable many-body problems "of goldfish type" is extended by including (the additional presence of) three-body forces. The solvable NN-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 tt\rightarrow\infty.

Keywords

Cite

@article{arxiv.1310.2335,
  title  = {Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces},
  author = {Oksana Bihun and Francesco Calogero},
  journal= {arXiv preprint arXiv:1310.2335},
  year   = {2013}
}